Stir together flour, 1 teaspoon salt, and nutmeg in a large bowl; make a well in center of mixture. Whisk together eggs and milk; gradually stir into dry ingredients, stirring until moistened. Let stand 10 minutes.
Divide dough into thirds on a heavily floured surface. Flatten each portion to 1/4-inch thickness, and cut with a wet knife into 4- x 1/8-inch pieces.
Bring 2 quarts water and remaining 2 teaspoons salt to a boil in a Dutch oven. Drop dough into water, and simmer 3 to 5 minutes or until dumplings float to surface. Remove with a slotted spoon.
Melt butter in a large skillet over medium heat; add dumplings, and sauté 2 minutes on each side or until golden. Sprinkle with breadcrumbs, and serve immediately.