Preheat the oven to 400 degrees F. Brush a shallow 2-quart baking dish (round or rectangular) with 1 tablespoon of the melted butter.
In a food processor, combine the cream cheese, sour cream, spinach, olives, artichoke hearts, mozzarella, Pecorino and 3/4 cup of the Parmesan. Then add the garlic, nutmeg, and salt and pepper to taste. Pulse to roughly chop.
Place dough balls around the edge of the prepared baking dish. Fill the center of the dish with the dip, spreading to even. Press any remaining dough balls into the top of the dip. Brush the dough with the remaining 2 tablespoons melted butter, and then sprinkle the dough and the dip with the remaining 1/4 cup Parmesan.
Bake until the dip is bubbling and the rolls are golden and cooked through, about 20 minutes.