Preheat the oven to 375 degrees F.
In a food processor, combine 1/2 cup of the mozzarella, 1/2 cup of the Parmesan, and the ricotta, sour cream and cream cheese. Blend until smooth, with no lumps of cream cheese. Spread the mixture into an even layer in the bottom of a 9-by-9-inch baking dish.
Mix together the fire-roasted tomatoes, tomato paste, garlic powder, Italian seasoning and red pepper flakes in a small bowl. Season with salt and pepper. Carefully spread the mixture over the cheese layer so that it evenly coats the cheese and you don't see any white. Top with the onions, bell peppers and sliced olives. Sprinkle the veggies with the remaining mozzarella and Parmesan.
Bake for 25 minutes; then turn the oven to 450 degrees F and bake until brown and crusty around the edges, another 5 minutes. Cool slightly. Serve with crusty bread.