Preheat the oven to 400 degrees, and brush a 9 by 13 casserole dish with 1 tablespoon of olive oil. Place prepared bell peppers in the dish, and set aside while you make the sauce.
Make the sauce: Heat remaining olive oil in a skillet on medium heat and saute onion until translucent, about 5 to 7 minutes. Add garlic and red pepper flakes. Once garlic is fragrant, add ground chuck and pork. Cook until meat has lost its pink color and begins to turn golden. Lower heat and add tomatoes and tomato paste and finish with chicken stock. Simmer until sauce thickens, approximately 15 to 20 minutes. Sauce can be stored for up to 7 days in the fridge.
Make the filling: In a medium bowl, combine ricotta, olive oil, salt, pepper, Parmesan, 1/2 cup mozzarella and most of the basil.
Assemble: Fill each pepper with 1/4 cup of the cheese mixture and top with meat sauce. Sprinkle each pepper with remaining mozzarella and bake for 25 to 30 minutes until cheese is melted and the mixture inside bubbles. If needed, broil for 5 to 6 minutes to ensure golden cheesy goodness. Top with remaining basil and serve. Peppers will keep up to 4 days covered in the fridge.