Heat the olive oil in a large skillet over medium-high heat. Add the beef stew meat and brown it on all sides for about 5 minutes. Season with salt and pepper while cooking.
Transfer the browned beef to the slow cooker. Add the potatoes, mushrooms, carrots, onion, and garlic.
In a small bowl, whisk the flour into 1 cup of the beef broth until smooth. Pour this mixture into the slow cooker along with the remaining broth and tomato paste.
Stir everything gently to combine. Sprinkle the fresh thyme leaves over the top.
Cover and cook on low for 8 hours, until the beef is tender and the potatoes are cooked through but still hold their shape.
Taste and adjust salt and pepper before serving.