First off I keep homemade chicken broth in my freezer at all times. Here is the original from Alton Brown. I eventually tweek every recipe, this is how I make it now (so simple):
Cover chicken carcass with water in a large stock pot, make sure the lid fits well. If to much steam is allowed out it will boil dry. Place your stock pot on stove and bring it to a roaring boil. Once I get it on the stove and get the temp set I begin to shake my seasonings on top. I don't have measurements because I'm a by feel cook. I would say about 2tbs of dried onion, 1tbs of garlic powder, 1 1/2 tsp of whole pepper corn and honestly you can't measure the salt. I feel like I always put the same amount of salt and it comes out different every time. Now hang out while it comes to a boil.
Once your water is at a roaring boil turn it down to a simmer and let it simmer for at least 6 hours. I simmer mine from 8-10. Then I allow it to cool for several hours. "How do you do this in a day?" I simmer it overnight, turn it off when I get up and if you have to leave you can just put the whole thing bone and all in the fridge for up to a couple of days before you skim it. (Note original says to cool immediately in sink - I may have to start doing this part, I'd forgotten about it. Note 2: If you put it in refrigerator for more then a few hours it will become gel like. Just pop it back on the stove top for about 10 minutes and it's not to hot to work with but it begins to break that gel down.)
Ok now you want to strain or dip out all of your bone, skin, and seasonings. I do this several times to get mine very clean. At this point you are ready to separate and store. You can store however you choose, I suggest 2 cup increments. This is usually how much you need to cook with. I use my food saver. I lay them flat in the freezer for a few hours then you can store them in a manner that fits your freezer.
Now how to make sure you have the ingredients on hand to just whip out a batch of dumplings.
Put a whole chicken in a stock pot and boil for 1-2 hours. Or until it's done and the juices come out clear. I season mine just about like the stock. Now this also provides you with bone and seasoning for more stock to put up.
While that chicken is boiling on the stove make up several batches of dumpling dough. I don't have my recipe handy, but I believe this one is close enough. I do not leave it set for 8 hours to dry. I mix the dough and with my hands make a big circle, wrap it in wax paper and put it in a food saver bag. So how many is up to you. I do anywhere from three batches on up. This puts one on my table for dinner and two up in the freezer for that day your REALLY want chicken and dumplings but don't have the time or energy to do all this prep work.
Ok by now your chicken should be done (ok maybe not but work with me). As soon as you can separate you chicken do so. I try to split my chicken in half. I try to go ahead and shred it if I know I'm cooking it for chicken and dumplings. Again I use my food saver (miracle product as far as I'm concerned). Now I toss all skin and bones back into the stock pot and make more stock.
Yes it's really not fast the first time but take my word for it. That first time you come in and the chicken is shredded, the broth is made and the dough is mixed you'll thank me.
I put mine together something like this. I put 2-3 cups stock and 2-3 cups water in a stock pot (the less water you put the creamier it will be), bring this to a boil. While this is coming to a boil I roll out and cut my dumplings from my dough.