Prepare the Garlic Confit: Preheat your oven to 300°F (150°C). In a small oven-safe dish, place the whole head of garlic. Drizzle with olive oil and cover with foil. Roast in the oven for about 45 minutes, or until the cloves are soft and caramelized. Once done, let cool, then squeeze the garlic cloves out of their skins and set aside.

Marinate the Ribeye: In a large bowl, mix together balsamic vinegar, honey, minced garlic, salt, and pepper. Add the ribeye steaks, ensuring they are well coated. Cover and marinate in the refrigerator for at least 1 hour, or overnight for best results.

Sear the Steaks: Heat a large skillet over medium-high heat. Remove the steaks from the marinade, reserving the marinade for later. Sear the steaks for about 3-4 minutes on each side until they develop a nice crust.

Braised Cooking: Reduce the heat to low and add the reserved marinade and beef broth to the skillet. Cover and let the steaks braise for about 20 minutes, flipping halfway through.

Prepare the Gravy: In another saucepan, add the diced carrots and enough water to cover. Bring to a boil and cook until tender, about 10 minutes. Drain and add to a blender with the roasted garlic and a splash of beef broth. Blend until smooth, adjusting the consistency with additional broth if necessary. Season with salt, pepper, and fresh thyme.

Serve: Remove the steaks from the skillet and let rest for a few minutes. Slice the ribeye and serve on plates, drizzled with the rich carrot and roasted garlic gravy. Garnish with fresh thyme sprigs.