Preheat the oven to 400 degrees. Cut the top off the head of garlic, drizzle with 1 tablespoon olive oil, wrap in foil, and roast for 30 minutes until soft. Let it cool.
Add the beef stew meat, diced onion, sliced carrots, and cubed potatoes to the slow cooker.
Squeeze the roasted garlic cloves into the slow cooker. Add the beef broth, balsamic vinegar, rosemary, thyme, oregano, salt, and black pepper.
Stir everything to combine, then cover and cook on low for 8 hours.
Stir once more before serving to distribute the flavors.