Place milk and butter in a small saucepan, and simmer over medium heat until butter melts. Remove from the heat and allow to cool.
Dissolve the yeast in the warm water placed in a small bowl. Set aside.
Combine the eggs, sugar, and salt in a large mixing bowl, and mix until thoroughly blended. Gradually stir in the flour, alternating with milk and yeast mixtures. Gather the dough into a ball. Cover the bowl with a cloth, and let the dough rest 20 minutes.
Pour the chicken broth into a large pot. Bring broth to a boil over medium-high heat.
Meanwhile, sprinkle flour over a clean board or countertop. Turn the dough out onto the board and knead lightly until smooth and satiny, about 3 minutes. Add a little more flour if the dough is sticky. Roll out the dough to be about 1/2 inch thick. Use a butter knife to cut dough into 2 inch wide strips, and place strips into the boiling broth. Dumplings will initially sink, then rise to the surface when cooked, about 10 minutes. Remove dumplings from the broth with a slotted spoon, and drain on a plate.