Mix ground chicken, onion, salt, and pepper together in a bowl.
Sift all-purpose flour and 1/2 cup whole wheat flour together in a bowl. Add 1/2 teaspoon salt.
Whisk milk and egg together in a small bowl. Pour over flour mixture; mix until dough comes together.
Turn dough out on a lightly floured work surface. Knead, adding the remaining 1/2 cup whole wheat flour, until dough is elastic. Divide dough into 4 pieces.
Roll out 1 piece dough to 1/16-inch thickness. Cut into circles with a 2-inch cookie cutter or water glass. Place 1 teaspoon chicken mixture in the center. Brush edges with water. Fold over into a half-moon shape and seal edges. Repeat with remaining dough and chicken mixture.
Fill a large pot with water; add remaining 1/2 teaspoon salt and bay leaf. Bring to a boil. Cook pelmeni in batches until they float to the top, about 5 minutes per batch. Transfer to a platter using a slotted spoon.