Combine the flour, salt and pepper in a large Ziploc bag and then add the beef and shake well so all the beef has been covered by the flour.
Heat 1 tbsp oil and butter in a large cast iron (or heavy bottomed) pan over medium high heat. Once the butter has melted and is sizzling, add the beef and cook for about 4 minutes per side, until just browned. Remove beef and place on a plate.
In a large pot, heat the 1 tablespoons of oil over medium heat. Once hot, add the onions, carrots and celery. Sprinkle vegetables with a pinch of salt and saute for ten minutes (adding the minced garlic after five minutes) until onion is translucent and carrots have started to become tender. Add the minced thyme and stir to combine.
Then, add the beef to the vegetables along with the wine and bay leaf. Bring to a boil, then reduce to a slow simmer (low heat setting) and partially cover pot, leaving about a half inch open.
Slowly simmer beef for three hours. After three hours, the wine should have reduced to a thick, velvety sauce and the beef should be very, very tender. Season with the additional teaspoon of salt and a pinch of black pepper.
Near the end of the simmering process, heat the remaining tablespoon of oil in a saute pan. Add the mushrooms and a pinch of salt and saute for ten minutes until tender. Stir cooked mushrooms into beef at the very end.
To make the roasted potatoes, preheat oven to 375 degrees. Wash potatoes and chop into fourths. Lay potatoes on a foil lined sheet tray and drizzle with olive oil, then sprinkle with sea salt and pepper. Roast for 35 minutes, tossing occasionally, until crisp and golden.
To serve, remove bay leaf from beef and serve beef alongside roasted potatoes with an additional sprig of thyme.