Wash the beef cheeks and pat dry thoroughly. Trim away any silver membranes and tendons from the meat.
Season the cheeks with salt and pepper, then coat with flour. Heat the clarified butter in a large roasting pan over medium-high heat. Sear the cheeks for 3-4 minutes on each side until deeply browned. Remove and set aside on a plate.
In the same pan, add the diced carrots, celery, leek, shallots, and garlic. Cook over medium-high heat for about 5 minutes, stirring occasionally, until the vegetables begin to color. Stir in the tomato paste and mustard, then add the allspice grains, juniper berries, bay leaf, thyme, and rosemary. Cook for another 2-3 minutes until the mixture is darker and fragrant.
Pour in the port wine, scraping up any browned bits stuck to the bottom of the pan. Simmer for 8-10 minutes until the port is completely reduced.
Return the beef cheeks to the pan, nestling them into the vegetables. Pour in the beef stock until the cheeks are almost covered. Season again with salt and pepper. Cover the pan with a lid.
Braise in a preheated oven at 220°C (425°F) for 25 minutes. Then reduce the oven temperature to 160°C (320°F) and continue braising for 3 hours until the meat is very tender.
Remove the cheeks and arrange on a serving platter. Strain the braising liquid and vegetables through a fine sieve, pressing gently to extract all the liquid. If the sauce is too thin, simmer it in a saucepan over medium heat for 5-10 minutes to thicken. Pour the sauce over or around the beef cheeks.