For the bourguignon:

Preheat the oven to 300 degrees F.

In a 9 to 10-inch pot that is at least 4 inches deep, bring 1/4 cup cooking oil to smoking temperature. Season the meat with salt and black pepper. Over high heat, brown the meat in the pot in 2 or 3 separate batches and set aside. Reduce the heat, add the bacon to the pot and cook it until it begins to brown. Add the onions, carrots, and celery and sweat approximately 10 minutes over medium heat while stirring often. Add the tomato paste and allow it to brown and cook about 5 minutes. Add the flour while stirring constantly. Slowly incorporate the red wine into the pot, stirring constantly so that no lumps form. Add the stock and meat to the pot and bring to a simmer. Secure the thyme and bay leaves together with the butcher's twine and place it in the pot. Place a lid on top of the pot and put it into the oven for 2 1/2 to 3 hours, or until the meat is fork tender. Remove the lid and skim the top of any excess fat. The onions and mushrooms should be added right before serving.

For the potato gratin:

Preheat the oven to 350 degrees F.

In a large bowl, toss the sliced potatoes with salt and black pepper. Arrange them in layers in a greased 8 by 6-inch oven-proof baking dish. Pour the heavy cream over the layered potatoes. Place the dish on top of a sheet pan and then into the oven for 45 minutes. Remove the potatoes from the oven and turn the oven temperature to broil. Top the potatoes with the cheese and return to the oven for approximately 5 minutes, or just long enough for the cheese to melt and nicely brown. Serve alongside the Beef Bourguignon.