This is a great, simple recipe. The quality of the ingredients make the dish, so don't skimp. It's from 50 Ways to Feed Your Lover, an interesting cookbook with meals chefs have made for their significant others.
Halve, pit, and peel the avocado. Cut it into slices lengthwise and drizzle with freshly squeezed lime juice.
Season the filets mignons with salt and pepper. Flatten lightly with your hand. Use a heavy-bottomed saute pan on high heat, and coat it with the olive oil. When the oil smokes, add the filets and sear them for about two minutes on each side, just until brown. If you are using a large enough saute pan (and one that is oven-proof, ala Calphalon aluminum), simply remove the filets and add a small roasting rack to the pan. If not, transfer the filets to an ovenproof pan with a roasting rack.
Preheat to 350°F Finish cooking the filets in the oven for about 15 minutes for medium rare (they should still feel quite soft to the touch).
Serve with slices of avocado on top, sprinkle sea salt and drizzle with olive oil. Garnish with cilantro sprigs.
Serve with Cilantro Serrano Chile Rice, or any other risotto or rice of your choosing.