In a large heavy bottomed pot, heat olive oil over medium high heat. Liberally season the short ribs with kosher salt and pepper. Sear all sides of short ribs in pot, about 2 minutes a side. Remove to a plate and set aside. Pour oil out of the pot and turn heat down to medium.
Add butter to the pot, chopped onions and carrots. Saute for about 3-5 minutes until veggies are slightly tender. Add garlic and tomato paste. Stir to combine and cook until fragrant, about 30 seconds.
Add the can of tomatoes with juice to pot. Stir in red wine. Deglaze and scrap any brown bits on the bottom of the pot.
Add beef stock and bay leaves. Bring to a simmer. Add short ribs back to the pot and cover. Simmer on a consistent low temp for 3 hours.
Every stove varies, but for me I have to keep it on a higher low setting. You want a continuous simmer so short ribs can braise and break down.
Remove short ribs to a serving platter and continue to simmer the sauce while assembling. Fish out bay leaves and discard. In a separate pan heat 1 tablespoon olive oil over medium high heat. Add mushrooms and saute for 5 minutes until browned and tender.
Top sauteed mushrooms on short ribs.
Whisk together cornstarch and cold water in a small bowl until dissolved. Add cornstarch slurry into the sauce and stir until sauce is thickened. Turn heat off and spoon sauce over short ribs.
Serve on top of mashed potatoes and garnish with chopped parsley. Enjoy!