Prepare vegetables by cutting up the potatoes, carrots, and mushrooms in large chunks (about 1-inch pieces.) Set aside in a large bowl as you finish cutting them. Cut the onion last and place on top of the other vegetables.
Prepare the beef by trimming off any large portions of fat. Cut into large chunks (about 1 1/2 to 2-inch pieces.)
In your stew pot, heat 1 tbsp of butter and 1 tbsp of olive oil. Set over medium heat. (If you are using a crockpot, you will want to do this portion on the stovetop in a large skillet. Don't skip it.)
Lightly coat each piece of beef with flour and brown in the oil. Do this a few pieces at a time, leaving room for the beef to breathe. Add more butter and olive oil as needed. Pull browned beef and set aside in a medium bowl until all pieces are done. (If you are using a crockpot, you can pull the beef and add directly into the crockpot.)
Add the onions to your cooking oil. Saute until tender (about 10 minutes.)
Reduce heat to low. Add the tomato paste to the onions. Mix until onions are well-coated.
Add red wine to the onions. Stir and scrape the bottom of the pot until all the brown bits have been released. (If you are using a crockpot, transfer this mixture into your crockpot when done.)
Add the browned beef, potatoes, carrots, mushrooms, beef broth, bay leaf, salt, thyme, and black pepper to your stew pot. Stir.
Cook on low heat for 2-4 hours (or in a crockpot for 7 1/2 hours). Stir occationally to prevent burning on the bottom. The stew is considered done with the beef cubes are tender and the potatoes and carrots are soft.
Add in peas about 10 minutes before serving.
Serve with crusty bread.