In a large bowl, combine meat cubes, onion, dill, soaked bread, egg, salt and pepper. Let sit for 2 hours in refrigerator for flavors to combine.
Grind mixture through a meat grinder 2 times using a medium die. Mixture should be finely pureed and sticky. Cut rounds out of wonton wrapper. Fill each wrapper with 1/2 teaspoon of mixture. Fold over and make tortellini shape. Fold sides over. Place in large saucepan with boiling water and boil for about 3 minutes.
Serve in deep-dish plates. Divide mushroom slices, beet dice, mint leaves, and dill into between 8 dishes. Add 10 pelmini and pour over consomme.