Place peeled potato cubes in a medium pot. Cover with water and bring to a boil. Simmer potatoes 20 minutes, until tender. Remove from heat and drain any excess water.
Using an electric mixer, mash potatoes until creamy. Add egg and salt, mix well.
Mix in flour ½ c at a time until a smooth dough forms. (The amount of flour needed will depend on how moist your potatoes are.
Bring 2 qts of water to a boil in a medium pot. Add 1 tsp of salt to the water when it begins to boil.
Pinch off a portion of the dough and roll it into a 1” thick snake on a cutting board. Cut the dough on an angle into ½“ pieces.
Drop dumplings into boiling salt water a few at a time, so they are not over crowded. Boil for 3-5 minutes, until firm. Remove from water and place on a paper towel to drain. *
Melt the butter in a large skillet with high sides. Add the onions and saute over medium high heat until lightly golden, 3-4 minutes.
Add the broth and parsley. Simmer the mixture until the liquid has reduced, 10-15 min.
Serve boiled Kopytka topped with mushroom mixture. Sprinkle with breadcrumbs, if desired.
