Marinate beef cheeks with onions, carrot, garlic, thyme, and beer in the fridge for 12 hours.
Preheat the oven to 150°C.
Remove beef from marinade, pat dry, and season with salt and pepper while reserving the liquid.
Brown the beef cheeks in a hot casserole pan with olive oil and butter.
Return beef to the pan with the reserved marinade and beef stock.
Cover with a slightly ajar lid and cook in the oven for 4-5 hours.
Cook whole carrots with star anise, 100g butter, salt, sugar, and water for 20-30 minutes.
Strain the beef cooking liquid into a pan and reduce until thick enough to coat a spoon.
Whisk in the remaining butter and season the sauce.
Boil potatoes in salted water for 12-15 minutes until tender.
Drain potatoes and dry them over low heat for a few minutes.
Simmer butter and milk in a pan until the butter melts.
Pass potatoes through a ricer and beat in the hot milk mixture until smooth.
Serve the beef cheeks with mash, glazed carrots, and reduced sauce.