In a large bowl, combine 5 Tablespoons melted butter, cottage cheese, pinch of salt, eggs and enough flour to make a soft dough. Shape dough into a roll; cover and let stand 30 minutes.
Wash and dry apricots. Cut in halves; remove and discard pit. Place 1 sugar cube between each pair of apricot halves; set aside.
Bring water to a gentle boil; add 1 teaspoon salt.
On a lightly floured board, press or roll out dough to a 1/2-inch thickness. Cut into 2-inch squares. Place a stuffed apricot (2 halves with a sugar cube in the middle) in center of each square of dough. Press dough around fruit, covering completely. Add to gently boiling water; cook 8 to 10 minutes. Drain on paper towels; arrange on a platter.
Melt 1/3 cup butter or margarine in a medium skillet. Add breadcrumbs and 3 Tablespoons granulated sugar; sauté until golden brown. Sprinkle caramelized breadcrumbs over dumplings.