Heat a large skillet over medium heat and add the ground beef, onion, and garlic. Cook until the beef is browned and the onion softens, about 6 minutes. Drain excess fat.
Transfer the beef mixture to the slow cooker. Add the mushrooms, carrots, and potatoes.
In a small bowl, whisk together the red wine, beef broth, tomato paste, thyme, salt, and pepper. Pour this over the ingredients in the slow cooker.
Cover and cook on low for 7 hours or until the vegetables are tender.
In the final 30 minutes, stir the flour into 2 tablespoons of the cooking liquid to make a slurry. Add it back to the stew and stir to thicken.
Taste and adjust salt or pepper if needed. Sprinkle with fresh parsley before serving.