Heat the oven to 400 degrees. Slice the tops off both heads of garlic, drizzle with 1 tablespoon olive oil, and wrap in foil. Roast for 35 minutes until soft and golden, then set aside to cool.
Warm the remaining tablespoon of olive oil in a large pot over medium heat. Add the beef and cook until browned on all sides, about 6 minutes. Remove the beef to a plate.
Add the onion, carrots, and celery to the pot. Cook for 5 minutes until the vegetables soften.
Stir in the barley, thyme, salt, and pepper. Return the beef to the pot and pour in the beef broth. Bring to a boil, then lower to a simmer and cook covered for 45 minutes.
Squeeze the roasted garlic cloves into a small bowl and mash with a fork. Stir the mashed garlic and milk into the stew. Simmer uncovered for 10 more minutes until the barley is tender and the broth thickens slightly.