Preheat an oven to 180 C / Gas 4. Season the short ribs with salt and pepper and set aside.
Heat an oven-proof pot with a lid over medium-high heat. Stir in the olive oil and butter until the butter has melted. Stir in the onion and cook until the onion begins to soften, about 3 minutes. Add the leek and continue cooking until the onion and leek are lightly browned. Remove and set aside.
Brown the short ribs in the hot pot until browned on all sides, about 3 minutes per side. Once browned, sprinkle the reserved onions over the ribs, pour in the wine, beef stock, tomatoes and Bloody Mary mix. Nestle the carrot chunks among the ribs. Bring to a simmer, then cover and place into the preheated oven.
Braise in the oven for 2 hours, then add the mushroom caps, cover and continue cooking 1 hour more.
Beef short ribs can be purchased at your local butchers. You may need to pre-order them.
You can purchase Tabasco Bloody Mary mix online.