Remove the ribeye steaks from the refrigerator about 30 minutes before cooking to bring them to room temperature. Pat the steaks dry with a paper towel and season both sides with salt and pepper.
In a large cast-iron skillet or a heavy-bottomed pan, heat 1 tablespoon of olive oil over medium-high heat until it shimmers.
Gently place the seasoned steaks into the hot pan and sear undisturbed for approximately 4-5 minutes.
Carefully flip the steaks using tongs. Immediately add the butter, smashed garlic cloves, and optional thyme to the pan. Cook for an additional 3-4 minutes, basting the steaks with the melted garlic butter.
Use a meat thermometer to check for doneness: Rare at 125°F, Medium-rare at 135°F, Medium at 145°F. Adjust cooking time as necessary.
Transfer the steaks to a plate away from heat and let them rest for 5-10 minutes.
Slice the steaks against the grain, drizzle with garlic butter from the pan, and serve with lemon wedges.
Notes
Let the steaks rest after cooking for juicier meat.