Step 1

Pat the cubed meat dry with paper towels; season with salt and pepper. Toss the meat in flour.

Step 2

Heat a large Dutch oven over medium-high heat. Add 2 tablespoons oil. Add half the meat in a single layer without crowding, and brown on all sides, 5 to 6 minutes. Remove meat from pot, and transfer to a bowl. Add 1/3 cup of wine, and stir with a wooden spoon, scraping any browned bits on the bottom of the pan (if wine evaporates too quickly to scrape up browned bits, add some stock). Transfer cooking liquid to bowl with meat. Wipe pot clean, and repeat process with remaining meat.

Step 3

Heat remaining 2 tablespoons oil in Dutch oven, and add onions. Cook, stirring occasionally, until golden all over, about 3 minutes.

Step 4

Deglaze pan with remaining 1/3 cup wine, and return reserved beef and cooking liquid to pot. Add stock and tomatoes; season with salt and pepper. Bring to a boil. Reduce to a simmer, and cook, covered, for 1 hour and 15 minutes. Add carrots and mushrooms. Cook, covered, until meat and vegetables are tender, 45 to 50 minutes.