In a small saucepan, combine the peeled garlic cloves and olive oil. Heat over low heat, allowing the garlic to simmer gently for about 45 minutes to 1 hour, or until the garlic is tender and lightly golden. Remove from heat and let cool.

Preheat the oven to 375°F (190°C). Place the halved shallots on a baking sheet, cut side up, and drizzle with a little olive oil. Roast in the oven for 25-30 minutes, or until soft and caramelized. In a mixing bowl, combine the roasted shallots, softened butter, lemon juice, and a pinch of salt. Mix until well combined and set aside.

Preheat a skillet or grill pan over medium-high heat. Season the ribeye steak generously with salt and pepper. Using a fork, mash a few cloves of the garlic confit to create a paste. Spread the garlic paste evenly over the surface of the steak, then press the chopped fresh thyme leaves onto the surface.

Place the ribeye in the hot skillet or grill pan. Cook for about 4-5 minutes on each side for medium-rare, adjusting the cooking time to your desired doneness. Use a meat thermometer to check for an internal temperature of 130°F (54°C) for medium-rare.

Remove the ribeye from the heat and let it rest for about 5-10 minutes. Top with the roasted shallot butter and garnish with fresh thyme sprigs. Serve with your choice of side dishes.