Start by removing the ribeye steak from the refrigerator and letting it sit at room temperature for about 30 minutes. Pat the steak dry with paper towels to remove excess moisture.
Season both sides of the steak generously with coarse salt and freshly cracked pepper.
In a cast-iron skillet, heat 2 tablespoons of olive oil over medium-high heat until it shimmers.
Carefully place the ribeye in the skillet and allow it to sear without moving it for about 4-5 minutes.
Flip the steak using tongs. Add the peeled shallot, garlic cloves, thyme sprigs, and butter to the skillet. Baste the steak with the melted butter.
Cook the steak for an additional 4-5 minutes, basting frequently. Use an instant-read thermometer to check for doneness.
Once cooked to your liking, remove the steak from the skillet and let it rest for at least 5-10 minutes.
Slice the ribeye against the grain and serve it with the roasted shallot, garlic, and a drizzle of the pan juices.