Place the chicken in a large pot at least 7qt. I use my gumbo pot. This recipe makes exactly 5 quarts and you want a little room. Cover the chicken with 4 quarts of water. Add bay leaves, salt, pepper, poultry seasoning, one of the onions quartered, and 3 celery stalks cut into large pieces. These will cook to the point of mush and be discarded later. Put the lid on and boil on medium heat( on my electric stove it is #5) for exactly one hour. Occasionally check to make sure it is at a medium boil and move the chicken around in the pot.
When the hour has passed turn off the heat, take off the lid and let it cool down for about 15 minutes. Then remove the chicken to a large bowl. Drain off any broth back into the pot. Cut the chicken down the center and open it up so it may cool. Set aside.
Next I strain the broth. I like to have a nice clean broth free of bay leaves, bones, skin etc. If you notice any chicken skin stuck to the pot please remove it. Throw it all out including the mushy onion and celery .Pour your nice broth back into the pot. Chop your remaining onion and celery into nice, pretty small pieces. Add it to your broth, put the lid back on and boil on medium heat while you are making your dumplings.
Now is a good time to clean up your mess. Once clean, you will need a nice floured surface about as long and wide as your rolling pin. If you don't have a rolling pin you can use a glass. The area should be about 15x15.
In a large mixing bowl add your 5-cups of flour. Make a well in the middle and pour in the 2 cups of milk. Mix well with a fork until all of the flour is moistened and you can make it all stick together in a dough ball. It is better to have a little dry flour in the bowl than to have dough that is too wet. If you really think you need to add milk do it by spoonfuls. Plop the dough out onto your floured surface, roll it around so that the bottom of the dough gets floured and then flip it over and roll the top around in the flour. Use your rolling pin or glass to roll the dough out. If it sticks just sprinkle a little flour on the sticky spots. Roll it out to a 1/4 inch thickness which should cover about a 15x15 area. Push in any raggedy ends. Use a knife to cut the dough into about 1 1/2 inch strips to have nice big dumplings like mine (pictured) or smaller if you like.
At this point take the lid off of the pot. The broth should be at a medium simmer--you need to see bubbles before adding your dumplings. Now cut each strip of dough into 1 inch squares. Throw each dumpling in the pot as you cut it. After each row stir the pot. Continue until you have cut all of the dumplings.( It is good for the dumplings to be coated with the extra flour, don't shake it off. This adds thickness to the broth.) Stir well making sure all of the dumplings are separate.Put the lid on and lower the heat. You want a low simmer.
Now it is time to remove the chicken from the bone. Separate the breast meat into medium sized chunks.Everything else usually comes off in bite sized pieces. Please make sure you are free of bones, fat and skin. By the time you have all of the chicken removed it is time to add it to the pot.
Remove the lid and add the chicken .Then add the cream of chicken soup, butter and parsley. Stir well. You may think your broth looks a little thin. Don't worry, it thickens upon standing. First you need to cook your chicken and dumplings a few more minutes now that everything is in the pot. I like to taste test about now and I usually add a little more salt, pepper, and poultry seasoning to suit my taste. Let this sit on the stove uncovered over very low heat for about 15 minutes. Then turn off the heat completely and let it sit for another 15 minutes. This is when it really thickens up for you. When it is cool enough and thick enough ---eat up!