Preheat oven to 350 degrees F. In a large bowl stir together mozzarella cheese, yogurt, mayonnaise, 2 tablespoons of the Parmesan cheese, the flour, and mustard. Stir in spinach, roasted red peppers, and 2 tablespoons of the green onions. Spread mixture evenly into an ungreased 1-quart ovenproof shallow dish or a 9-inch pie plate. Sprinkle with the remaining 2 tablespoons Parmesan cheese.
Bake, uncovered, for 15 to 20 minutes or until edges are bubbly and mixture is heated through. Sprinkle with the remaining 2 tablespoons green onions. Serve with sweet pepper strips, crackers, and/or flatbread.