Preheat oven to 350° F. In a large bowl, combine cream cheese and yogurt. Stir until well combined. Stir in 1 cup of mozzarella, 2 tbsp of parmesan, garlic, spinach, artichokes, black pepper, and red pepper. Mix until well combined. Transfer to an 8x8 casserole dish and spread evenly. Sprinkle remaining mozzarella and parmesan cheese over the top. Bake for 30 minutes until edges are golden and dip is heated through. Serve warm.