Trim the beef cheeks of any sinew and slice them around 15mm (½") thick.
Season the beef generously with salt and pepper.
Heat half of the cooking oil in a 30cm or 12" frying pan over a medium-high heat and sear the beef cheeks on both sides, and then transfer to a 4 litre (4 Quart) slow cooker. If you are cooking this on the stovetop, sear them in a 24cm (10") Dutch oven, then remove and set aside.
Peel the garlic and bash it with the side of a knife.
Peel the onion and chop it into large 2-3cm (¾-1¼") chunks.
Cut the celery into roughly the same-sized pieces as the onion.
Return the pan to the heat and add the garlic, onion, carrot and celery.
Fry for 3-4 mins to start getting some colour, then either transfer them to the slow cooker with the beef or return the beef to the Dutch oven.
Add the flour to the beef and vegetables and stir to coat.
If you are cooking in a slow cooker, deglaze the frying pan with the beer, then pour it over the beef. If you are cooking in a slow cooker, pour in the beer and bring it to a boil.
Add the beef stock and Worcestershire sauce and stir.
Transfer to the oven and bake at 150°C or 300°F for 3-4 hours or in a slow cooker for 6 hours on low or 4 hours on high.
An hour before serving, cut your large mushrooms in half, then peel and cut the shallots in half lengthways, removing most of the root.
Add the other half of the oil to a 30cm or 12" frying pan and sear these vegetables on the cut side only. Then transfer them to the beef pot and cook for another 45-50 minutes.
When you are ready to serve, strain the cooking gravy through a fine mesh sieve into a hot frying pan and reduce by 10-15%.
Pull out the beef (carefully, it will fall apart), shallots, mushrooms, and carrots for serving, then push any liquid out of what remains before discarding the pulp in the sieve.
Mix the cornstarch with a tablespoon of water and whisk it into the gravy and cook until you have the desired thickness, return the solids and serve.