Preheat oven to 350 degrees.
In food processor, combine the mozzarella, sour cream, 2 tablespoons Parmesan, pepper, garlic, and the cream cheeses until smooth. Pulse or stir in the artichokes and spinach.
Spoon mixture into a 1 1⁄2-quart baking dish. Top with remaining Parmesan. Bake for 30 minutes or until golden brown and bubbling.