Heat the olive oil in a large skillet over medium-high heat. Add the beef cubes and brown them on all sides for about 5 minutes. Transfer the beef to the slow cooker.
Add the diced onion and minced garlic to the same skillet. Cook for 3 minutes until the onion softens. Stir in the tomato paste and flour, then cook for 1 minute more.
Pour the red wine into the skillet and scrape up any browned bits. Let it simmer for 2 minutes, then transfer everything to the slow cooker.
Add the mushrooms, carrots, beef broth, salt, pepper, and thyme sprigs to the slow cooker. Stir to combine.
Cover and cook on low for 7 to 8 hours until the beef is fork-tender. Remove the thyme sprigs before serving.