Mix flour, salt, nutmeg, paprika, and pepper together in a bowl. Roll chicken breasts in the mixture.

Preheat the oven to 325 degrees F (165 degrees C).

Heat olive oil in a large skillet over medium heat. Add chicken; cook until browned, about 5 minutes per side. Place chicken in a deep casserole dish with a cover.

Place carrot, onion, celery, and garlic in the same skillet. Reduce heat to low. Cook and stir until slightly tender, about 10 minutes. Place vegetables in the casserole dish on top of the chicken. Pour hot water over the mixture.

Bake in the preheated oven until chicken is no longer pink at the bone and the juices run clear, about 1 1/2 hours. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C). Bone chicken breasts and cut into bite-size bits.