• Remove the filets from the refrigerator to allow them to come to room temperature (about 30 minutes). After 30 minutes, drizzle the steaks with olive oil and season on both sides with salt and pepper.
• Position a rack in the center of the oven and preheat to 400°F. Line 2 small baking sheets with aluminum foil and coat them with nonstick spray. Note: Be sure to choose baking sheets small enough to fit in the oven side by side.

Make the shallot butter

• Use a fork to thoroughly combine the softened butter, minced shallot, and parsley on a flat plate. Transfer the mixture to a sheet of wax paper and form it into a 1-1/2-inch diameter cylinder. Roll tightly and freeze for 10 minutes to solidify, then refrigerate until ready to use.

Prepare the lobster tails for cooking

• Place the lobster tails on a cutting board with the shell side facing up. Using kitchen shears, carefully insert the tip just under the shell, making sure not to cut into the meat. Cut a straight slit down the center of the shell, stopping before you reach the fan at the end of the tail. Turn the lobster tails over and use the shears to snip off the small flippers.
• To loosen the lobster meat from the shell, turn the tail over and insert an upside-down teaspoon between the shell and the meat. The spoon’s smooth, rounded shape helps separate the meat without tearing it.
• Turn the lobster tail shell-side up and gently spread the shell open along the cut. Carefully lift the meat, pulling it upward while keeping it attached at the fan end. Press the empty shell halves together, then lay the meat on top of the shell. If you see a dark vein running along the length of the meat, use the tip of a paring knife to remove it and discard it.
• Rinse the lobster tails under cool water, then gently pat them dry with paper towels. Place them on one of the prepared baking sheets and squeeze a little lemon juice over each tail. Cut a pat of shallot butter for each lobster tail, then slice it in half. Place both pieces end-to-end on top of the meat. Set aside.

Cook the filet mignons

• Heat a heavy frying pan over medium-high heat and add a small amount of olive oil to coat the surface. Place the steaks in the pan and sear for 1 to 1-1/2 minutes per side, until they release easily from the pan.
• Once seared, transfer the filets to the remaining prepared baking sheet and place them in the oven. For medium-rare (recommended), the filets will need about 5 minutes in the oven. However, after 3 minutes, add the lobster tails to the oven so they're ready to serve together.
• After a total of 5 minutes of cooking time, check the internal temperature of the filets with an instant-read thermometer. For medium-rare, it should read 125°F. Remove the filets from the oven and let them rest, uncovered, for 5 minutes before serving.

Cook the lobster tails

• Timing Note: After the filets have been in the oven for 3 minutes, add the lobster tails. They will need 6 to 8 minutes to cook fully.
• Keep a close watch on the lobster tails. If you remove the filets from the oven after 5 minutes, the lobster should be ready just as the filets finish resting.

Plate and serve

• Place each filet and lobster tail on individual plates. Top the filets with a pat of compound butter and serve immediately.