Preheat oven to 400°F. Slice top off garlic head to expose cloves, drizzle with 1/2 tablespoon olive oil, wrap in foil, and roast for 35-40 minutes until soft and golden. Cool, then squeeze out cloves and mash into paste.
Pat ribeye steaks completely dry with paper towels. Season both sides generously with salt and pepper. Let sit at room temperature for 20-30 minutes.
Heat cast-iron skillet over medium-high heat. Add 1 tablespoon olive oil. Once shimmering, add steaks and sear for 4-5 minutes without moving.
Flip steaks and cook 3-4 minutes more for medium-rare (130°F internal). In last minute, add 1 tablespoon butter and baste steaks continuously.
Transfer steaks to cutting board, tent with foil, and rest for 8-10 minutes.
Reduce pan heat to medium. Add remaining 2 tablespoons butter. Add mashed roasted garlic and cook for 1 minute, stirring.
Pour in beef broth and scrape up browned bits from pan bottom. Simmer 2-3 minutes until slightly reduced.
Stir in fresh thyme and rosemary. Simmer 1 minute more. Season with salt and pepper. Sauce should coat back of spoon.
Slice steaks against the grain. Serve topped with roasted garlic pan sauce. Garnish with fresh parsley.