Pat beef stew meat dry with paper towels. Do not season. Heat 1 tablespoon olive oil in a Dutch oven over high heat until shimmering. Add half of beef and cook until well browned on all sides, about 8 minutes. Reduce the heat if oil begins to smoke or fond begins to burn. Transfer beef to the slow-cooker.
Repeat with remaining beef and 1 tablespoon olive oil, then add to the slow-cooker.
Add 2 teaspoons olive oil to the now-empty Dutch oven if needed, add the onion and carrots. Cook, scraping bottom of pan to loosen any browned bits, until onion is softened, 3-4 minutes.
Add the gluten-free flour and cook, stirring constantly, until no dry flour remains, about 30 seconds. Add garlic and tomato paste and cook, stirring constantly, until fragrant, about 30 seconds.
Slowly add the red wine, scraping bottom of pan to loosen any browned bits. Increase heat to high and allow wine to simmer until thickened and slightly reduced, about 2 minutes. Whisk in the beef stock/broth.
Pour the stock/broth mixture into the slow-cooker. Stir in the bay leaves.
Cook on low for 4-6 hours (or high for 3-4 hours). Enjoy!