If the chicken breast fillets are frozen, thaw them completely. Cut the broccoli into small pieces and cook in water over medium heat for 4 minutes until tender-crisp. Cut the chicken breast fillets and bell peppers into small cubes.
Cut the onion into small pieces and mince the garlic. Heat oil in a large pan over medium-high heat, add the onion and garlic, and sauté for 2 minutes until fragrant. Add the chicken cubes and cook for 5 minutes until cooked through.
Add the pre-cooked broccoli and cook for 2 minutes. Add the bell pepper cubes and cook for 2 minutes more. Stir in the crème fraîche and cream, then simmer for 2 minutes. Remove from heat and season with salt and pepper to taste.
Preheat the oven to 180°C / 356°F with top/bottom heat. Transfer the mixture to a baking dish, sprinkle with the grated cheese, and bake for 12 minutes until the cheese is melted and golden.