Preheat oven to 320F.
Prepare the beef cheeks: cut off any large, fatty membrane. Pat dry then season each side with 1 tsp of salt and a good grind of pepper.
Heat 2 tbls olive oil in a large casserole dish with a lid over high heat. Sear the beef cheeks on each side until nicely browned. If neccesary, work in batches rather than crowding the pan. Remove beef cheeks and loosely cover with foil to keep warm.
Turn down the heat to medium high and heat the remaining 1 tbsp of olive oil. Add garlic, onion and carrots. Sauté for 3 minutes until onion becomes translucent, then add the celery and sauté for a further 3 minutes.
Pour the wine into the casserole dish and stir to scrape the brown bits off the bottom. Bring wine to simmer for 1 minute.
Add remaining ingredients (including 2 tsp salt).
Cover and cook at 320F for 3 to 3½ hours until the cheeks are very tender. Turn at least once during cooking.
Open the casserole dish and remove the beef cheeks. Discard the thyme stems and bay leaves.
Use a handheld stick blender to puree the braising liquid into a smooth Sauce – it will change from a dark brown to a lighter brown color.
Bring the sauce to simmer over medium heat and simmer until it turns a darker brown color and reduces by about ¼ to ⅓, to a gravy consistency – about 3 to 5 minutes.
Season to taste.
Remove from heat, return beef cheeks to the sauce, let cool.