Spread the peppercorns onto a plate. Season the filet mignons on all sides with salt.
Press the steaks in the peppercorns on one side only to create a peppercorn crust.
Heat a large saute pan over high heat. Turn your broiler to high heat.
Add the oil to the preheated pan. Just before the oil begins to smoke, add the steak to the pan, peppercorn-crusted side down.
While cooking over high heat, use tongs to flip the steak every 30 seconds. Continue flipping for about 4-5 minutes for medium rare. If you’d like your steak cooked more or less, simply increase or decrease the amount of cooking time.
Just before the steak is finished, turn the heat to medium-low and add the remaining 2 tablespoons of butter to the pan. Smash garlic clove and add it to the pan, along with the thyme. Use a metal spoon to baste the steak for about one minute.
Remove the steak from the pan and set aside on your cutting board, topped with garlic and thyme, to rest.
Meanwhile, transfer the lobster tails to your oven to broil until cooked through, about 3-5 minutes.
Stir the sliced chives into your finished sauce. Season with salt.
Plate the filet mignons on two serving plates, topped with the halved lobster tails. Spoon on the sauce. Serve alongside your favorite potato preparation and enjoy!!