Preheat your oven to 300°F (150°C). In a small baking dish, combine the peeled garlic cloves with olive oil. Cover the dish with aluminum foil and roast in the oven for about 45 minutes, or until the garlic is soft and lightly golden. Set aside.

In a bowl, whisk together the aged balsamic vinegar, honey, salt, and pepper. Add the ribeye steaks, ensuring they are well coated. Let them marinate for at least 30 minutes at room temperature.

In a large skillet over medium-high heat, add a touch of olive oil. Remove the steaks from the marinade, letting the excess drip off. Sear the steaks for about 4-5 minutes per side for medium-rare, or until desired doneness. Remove from the skillet and let rest.

In the same skillet, add the chopped carrots and sauté for about 5 minutes, until they start to soften. Cut the head of garlic in half horizontally and add it to the skillet. Pour in the beef broth, scraping up any browned bits from the bottom of the pan. Stir in the fresh thyme and rosemary. Bring the mixture to a simmer and cook for about 15-20 minutes, until the carrots are tender.

Once the carrots are soft, remove the skillet from heat. Using an immersion blender, blend the mixture until smooth. If you prefer a chunkier gravy, blend just until combined, leaving some texture. Return the gravy to low heat. Stir in the roasted garlic from the confit and the optional butter for added richness. Season with salt and pepper to taste.

Slice the rested ribeye steaks against the grain. Serve topped with the rich carrot and roasted garlic gravy, and drizzle with any remaining balsamic marinade from the steaks.