Heat a large, heavy skillet over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Add half of beef; cook 8 minutes or until well browned, turning to brown on all sides. Place browned beef in an oven-proof pot; sprinkle with ⅛ teaspoon salt. Repeat with remaining 1 tablespoon oil, remaining beef, and ⅛ teaspoon salt. Set aside.
Melt butter in the same frying pan; add onions to pan; cook 1 minute on each side or until browned. Add onions to the oven-proof pot.
Add garlic to pan; sauté 1 minute. Add tomato paste; cook 1 minute, stirring constantly. Add 1 cup wine, scraping pan to loosen browned bits; cook 2 minutes or until half of liquid evaporates. Add stock and pepper; bring to a simmer. Nestle thyme sprigs into liquid. Add beef into the pot; top beef mixture with mushrooms; scatter carrots over top.
Cover with a lid and cook in oven (300 degrees) for 3 hours, or until meat is tender.
Remove the thyme leaves; serve over mashed potatoes, brown rice, or quinoa.