In a large oven-safe pot or Dutch oven over medium heat, melt butter, and cook and stir carrots, celery, onion, and mushrooms until the vegetables start to become tender, about 10 minutes. Add Garlic and stir for about 1 minute. Season with salt, cayenne pepper, black pepper and paprika. Mix in flour, stirring to coat vegetables with flour, about 5 minutes. Add half of reserved stock, and stir with the vegetables and flour to form a very thick sauce. Stir in remaining stock until sauce is smooth; reduce heat to a simmer, and cook uncovered for 45 minutes.
Preheat oven to 400 degrees F (200 degrees C).
Stir half n half into the sauce, and gently mix in the reserved chicken meat, herbs de Provence, tarragon, and rosemary. Bring stew back to a simmer, and cook for 10 more minutes. Pop open the can of biscuits, separate, quarter and place biscuits on top of stew.
Bake in the preheated oven until the biscuits are golden brown and the stew is bubbling, about 20 minutes. Place lid on the pot or Dutch oven, and return to oven; bake until biscuits are cooked through, about 15 more minutes. Test biscuits for doneness by pulling apart a biscuit near the middle of the stew to see if it’s cooked through.