This recipe can be one or two days long, depending on your choices.
You'll need:
1 whole chicken
celery
carrots
onions
salt
pepper
matzoh meal
eggs
Prep
 your chicken for roasting- sprinkle the skin with some salt and pepper,
 then put in a 350 degree oven for 15 minutes per pound. If it's a 
little underdone, that's okay, it'll finish cooking in the soup anyway. 
Take the chicken out of the oven and set aside. Remove all the fluids 
and put into a pyrex cup in the fridge for an hour or so.
By
 this point, the chicken should have cooled. Set up two bowls, one for 
the meat, and the other for everything else- bones, skin, everything. 
Put the meat aside, and dump all the bones and scraps into a pot. 
They'll be the base for your stock. 
Roughly
 chop carrots, onions, and celery into the stock pot. These are used for
 flavoring, not for eating (unless you really want to...) so don't worry
 about anything more than a rough chop- quarter the onions with the skin
 on, half or quarter the carrots and celery. How much is up to you- I 
recommend being restrained with the carrots, as they have a lot of 
sugar, and the sweetness can overwhelm the soup. For a large soup pot, 
one of those giant costco onions, 4-6 stalks of celery, 3 carrots should
 be fine. 
Add cold water until it is an 
inch below the top, then put the pot on to heat. You'll want something 
like a hard simmer/light boil, so a medium heat usually works. Let it 
keep going until an inch or so of water has evaporated- roughly speak, 
boiling for an hour or two. Give it a taste- the flavor won't be hugely 
strong but you'll know it when it's ready.
Separate
 the solids. If you really want to go crazy, you can use fine filters 
and such, but I tend to use a slotted spoon to get all the big stuff and
 a wire mesh ladle I have to finish.
You have 
an option now. If you want, you can stick the stock in the fridge 
overnight to solidify the fat and scum to scrape away. If you want to do
 this, now is the time, it's easiest. Otherwise, you can continue, but 
when uneaten soup is put int he fridge, it'll develop a layer on top. 
Not a big deal, but a little trickier to deal with to remove if you want
 to when there are soup components inside. If you do refrigerate 
overnight, put the meat you set aside into a ziplock bag and keep in the
 fridge overnight.
You now have your 
chicken stock- this is incidentally a great way to make stock for all 
kinds of things, so any time you roast chicken or something, it's a nice
 little something extra to do to make your own stock for dishes.
Set
 the stock pot on the stove to start heating, again to a light boil. 
Ready your chicken and vegetables (the same carrots, celery, and onions,
 but now cut for eating sizes) in amounts you feel comfortable with. 
While the stock pot is heating, prep your matzoh meal.
Now,
 I've had difficulty with this in the past. I always used to use manischewitz, but it got hard to find and I switched to streitz. I got 
leaden balls- sinkers, not floaters. Tonight I had a box of each and I 
ended up going to manischewitz, but in case it made a difference, I also
 added an extra egg. The balls came out perfectly- whether it's the 
brand or the extra egg, I couldn't say. I don't see any harm in adding 
the extra egg tho. If you like sinkers, that's fine too, but my family has always been firmly in the floater party.
You'll prep the matzoh ball 
mix similar to how it says on the box. Typically that will mean one pack
 of the meal, two eggs, and some oil or butter. We're going to make a 
couple of changes though. As I said before, add an extra egg. For the 
fat, instead of butter or oil, go to that pyrex cup I told you to put 
aside earlier. There should be a nice layer of fat on top, 3-4 
tablespoons worth. Scrape that off and place in your small bowl and give
 it five minutes to come to room temperature. Then add your matzoh meal.
 Then add your three eggs. Whip together with a fork until uniform, then
 place in the fridge for 15 minutes.
By now, 
the stock pot should be boiling. Lightly salt and pepper the stock. You 
can add the rest of your solids now (further flavoring the soup) or wait until the matzoh balls are 
done, up to you.
Take the matzoh ball mix out 
of the fridge. Take enough to roll a ball about the diameter of a penny-
 they blow up to several times their size, so don't listen when the box 
says to make them an inch in diameter. You want maybe a half inch. Roll 
and drop into the rolling stock, roll and drop. This should be pretty 
quick, when you're done, you may see that not only have they started to 
balloon in the stock but that some of the first ones you did are 
darkening. Give them a gentle stir to turn them all over (that 
discoloration is from them drying out on that side, then cover the 
stockpot with a lid. Cook for 20 minutes, then uncover and add the rest 
of the solids if you haven't already.
Dump your solids in and add a
 little salt and pepper- you aren't done yet, so undersalt and 
underpepper. It will concentrate and develop and it's too easy to 
oversalt and overpepper. 
Let it all cook for another hour or so, then do your final salt and peppering. Serve immediately.
You
 also have the option to cook the matzoh balls in a separate pot of 
water, sometimes salt water. I prefer to cook them in the stock so they 
take up the flavor of the stock. It's personal preference, but some 
folks find it easier to deal with and prefer the taste.
Also,
 this freezes really well. I always like to have some in the freezer, 
because when I'm sick is when I want and need it the most, but I'm least
 able to make it. Wheras when frozen, you can easily just dump the 
frozen block into a pot, add a little water and cover, turn the heat on 
low and have nice hot soup ready to go.