In large plastic food-storage bag, combine 1/3 cup flour, salt, black pepper and cayenne pepper. Shake to mix.
Add rabbit pieces. Shake to coat.
In large skillet, heat 1/4 inch of oil over medium-high heat until hot.
Add coated meat and brown on all sides.
Reduce heat and cover tightly. Cook over very low heat until tender, about 20-25 minutes. Turn pieces once.
Remove cover and cook 5 minutes longer to crisp.
Transfer meat to plate lined with paper towels and set aside to keep warm.
Discard all but 3 tablespoons of the oil.
Over medium heat, stir 3 tbsp flour into reserved oil. Blend in milk or broth. Cook over medium heat, stirring constantly, until thick and bubbly. Add salt, pepper and brown bouquet sauce to taste.
Serve and Enjoy!