The night before cooking, season the goat breasts with the salt and pepper and the chopped herbs all over, pressing to make sure everything adheres to the meat. Allow the meat to marinate overnight, covered.
The next day, preheat the oven to 300. Combine the carrots, onion, celery, garlic and stock or water in a baking dish. Put the goat breasts in the dish, meat-side down, top with a piece of parchment and bake, covered with foil until the breasts are cooked and soft, about 3 hours. Remove the breasts from the oven and cool to room temperature, then transfer the breasts to a cutting board.
Gently remove the rib bones from the breasts, saving any meat that falls off while you’re working with them. If you see very large deposits of fat, remove or trim them, but make sure not to try and remove all of the fat or the breasts will break into pieces, you want to keep the breasts as whole as possible.
Put any meat that’s fallen off the breasts back on them, then wrap in plastic, put in container wide, shallow container and press with a weight overnight, or at least until cold.
When the breasts are chilled and you want to cook them, preheat the oven to 350, remove the breasts from the fridge, unwrap, season lightly with salt and pepper, then cut each breast on a slight diagonal into 6 triangles. Bread each slice of breast in flour, egg, and then breadcrumbs, then transfer to a baking sheet and bake until hot throughout, about 10-15 minutes. Serve immediately with the warm tomato sauce and a salad of watercress dressed with good oil, lemon, salt and pepper.
Notes
You can change the garnishes how you like here. Spicy tomato sauce is my favorite, but aioli, hot sauce, or your favorite sauce will be fine.