Pat filet mignon dry on both sides with paper towel, and season with salt and pepper, allow to come to room temperature about 30 minutes.
Preheat oven to 225°F, place filet on wire rack lined sheet rack, and put an internal meat probe in the center of the filet. Roast until it reaches 5° below your desired temperature doneness.
Place olive oil in cast iron pan, bring to high heat and get a hard sear on filet; add thyme, rosemary, garlic, and butter to pan; flip filets.
Baste filet with butter, about 30 seconds and remove from pan; allow to rest for 7 to 8 minutes, then slice into 1” medallions.
Plate orzo pasta on the bottom of plate, topped with filet medallions, and finished with caponata.