Season beef with salt and pepper. Heat 2 tablespoons oil in a large Dutch oven over medium-high; brown beef in batches. Remove; set aside.
Add 1 tablespoon oil to same pot; sauté all mushrooms about 8-10 minutes until golden brown and liquid evaporates. Set aside with beef.
Add remaining tablespoon oil and butter; sauté onion about 5 minutes until softened. Add garlic; cook 1 minute until fragrant.
Stir in tomato paste and flour; cook 1 minute. Add wine, scraping browned bits, then broth.
Return beef with thyme and bay leaves; boil, reduce heat to low, cover, and simmer 1 hour.
Add carrots and potatoes; cover and simmer 30 minutes until nearly tender.
Stir in mushrooms; cook uncovered 15-20 minutes until everything is tender and stew thickened. Remove thyme and bay leaves; adjust seasoning and garnish with parsley.