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Pat filet medallions dry. Season both sides with salt and pepper.
Heat a cast iron skillet over medium-high heat.
Add olive oil to the pan. Cook for 3 minutes without disturbing the steaks. Flip and cook for an additional 2 minutes, or until the steak internal temperature reaches 135F for medium rare.
After you flip the steaks, add the butter and rosemary to the pan. Spoon butter over steaks while the steaks finish cooking.
Remove steaks from pan and let rest for 10 minutes, then serve.