Preheat the oven to 375°F (190°C) and lightly grease a baking dish.
Heat the olive oil in a large skillet over medium heat. Cook the onion and garlic until softened.
Add the chicken and bell peppers. Cook until the chicken begins to lose its raw color.
Stir in the tomato paste, tomato sauce, oregano, paprika, salt, and black pepper. Simmer until the chicken is cooked through and the sauce thickens slightly.
Boil the pasta in salted water until just under al dente. Drain well.
In a saucepan, melt the butter over medium heat. Add the flour and whisk for 1 minute.
Slowly pour in the warm milk while whisking until smooth.
Season the béchamel with salt, black pepper, and nutmeg. Cook until thick and creamy.
Combine the cooked pasta, chicken sauce, and béchamel until fully coated.
Transfer to the baking dish and spread evenly.
Top with mozzarella and cheddar cheese.
Bake for 20 to 25 minutes until bubbly and lightly golden.
Rest for 5 to 10 minutes before serving.