Place whole chicken in a large stockpot and cover with water.
Add 2 ½ tsp salt.
Bring to a boil and then reduce heat to a simmer, and cook for 1 ½ hours or until chicken is done.
Remove chicken, place on a cutting board, and let cool to the touch. Reserve broth.
In a separate bowl, mix together flour and 1 ½ tsp salt.
Cut in fat. I just mix and pinch with my fingers until well cut in.
Add water and mix.
Turn out onto a board and knead until it come together in a ball.
Divide dough into fourths.
One at a time, roll out until very thin and cut into strips approximately 1.5 in x 4 in long.
Drop into pot of boiling broth in which the chicken was cooked.
Cook for about 15 minutes or until dumplings are tender but not falling apart.
While dumplings are cooking, debone chicken and add at least half of the chicken back into the pot. You can use the whole chicken if you wish, but I like to save the other half for another meal.
Taste broth for salt, and add additional salt and pepper if desired.
Optional: Stir in milk right at the end to create a white silky broth. This is not necessary, but it's how my grandma does it.