Preheat oven to 375 degrees F. Coat a 6-cup baking dish or pan with cooking spray.
Heat oil in a medium skillet over medium heat. Add onion, garlic and crushed red pepper; cook, stirring occasionally, until just starting to caramelize, 6-8 minutes.
Stir in tomatoes, beans, and Italian seasoning and remove from heat.
Meanwhile, combine 1/2 cup mozzarella, ricotta and 2 tablespoons basil in a medium bowl. Set aside.
Spread 1/2 cup of the tomato mixture in the prepared baking dish. Top with the ricotta mixture, then sprinkle evenly with chicken. Spoon the remaining tomato mixture on top, and sprinkle with the remaining 1 cup mozzarella.
Bake until bubbly and the cheese has melted, 25 to 30 minutes. Let stand for at least 5 minutes. Serve hot or warm, topped with the remaining 1 tablespoon basil.