Season beef cubes with salt and pepper. Heat 2 tablespoons olive oil in a large Dutch oven over medium-high heat and brown beef in batches. Remove and set aside.
In the same pot, add 1 tablespoon oil and sauté all mushrooms until golden brown and their liquid has evaporated, about 8-10 minutes. Remove and set aside with beef.
Add remaining tablespoon of oil and butter to the pot. Sauté onion until softened, about 5 minutes. Add garlic and cook for 1 minute until fragrant.
Stir in tomato paste and flour, cooking for 1 minute. Pour in red wine, scraping up browned bits, then add beef broth.
Return beef to pot along with thyme sprigs and bay leaves. Bring to a boil, reduce heat to low, cover, and simmer for 1 hour.
Add carrots and potatoes, cover, and simmer for 30 minutes until vegetables are nearly tender.
Stir in the reserved mushrooms and cook uncovered for 15-20 minutes until everything is tender and stew has thickened. Remove thyme sprigs and bay leaves, adjust seasoning, and garnish with fresh parsley.