Peel the onions and place in a large pot. Cover with water and bring to a boil. Lower the heat and simmer until tender, about 40 minutes.
While the onions are cooking, prepare the stuffing. Heat 1 tablespoon of the butter and the oil in a skillet. Saute the minced onion until limp and clear; do not brown. In a large bowl, combine the meat, minced onion, ½ cup of the bread crumbs, milk, egg, salt and pepper to taste, and parsley. Mix until well blended; set aside.
When the whole onions are cooked, remove from the water with a slotted spoon and drain on paper towels. When cool, strip off the large outer layers. Place 2 teaspoons of the meat mixture on the end of each onion strip and roll up. Continue until the meat mixture is gone.
Preheat the oven to 400 degrees F. Melt the remaining 3 tablespoons butter in a baking dish to coat the bottom and sides. Turn each onion roll in the butter, coating all sides, and bake for 15 minutes. Sprinkle with the remaining 3 tablespoons bread crumbs. Bake for 15 minutes more.