Put beef cheeks, garlic, thyme, wine, bay leaf, onion, celery, and clove into a bowl; cover and refrigerate 1–2 days. Transfer beef cheeks to a plate, reserving marinade. Pat beef cheeks dry and season with salt and pepper. Melt butter in a 6-qt. Dutch oven over medium-high heat. Working in batches, add beef cheeks and cook, turning, until browned, about 8 minutes. Transfer beef cheeks to a plate.
Heat oven to 325˚. Add reserved marinade to pot along with beef stock and calf's foot; boil for 5 minutes. Nestle beef cheeks in liquid and cover them with a sheet of parchment paper cut to fit the inside of the pot. Cover pot, transfer to oven, and cook, turning beef cheeks every hour, until tender, about 4 hours.
Using a slotted spoon, transfer beef cheeks to a plate and cover with aluminum foil. Skim fat from surface of cooking liquid. Set a fine strainer over a 2-qt. saucepan and strain cooking liquid, discarding solids. Bring to a boil over high heat and reduce until liquid has thickened and coats the back of a spoon, about 15 minutes.
Transfer beef cheeks to a clean dutch oven. Pour sauce over beef cheeks and add mushrooms, bacon, pasta, onions, and carrots. Cover pot and bake until vegetables and beef are warmed through, about 10 minutes. Serve hot and garnished with parsley.
