Allow the steaks to sit at room temperature covered with plastic, for at least 30 minutes to an hour before cooking. This will help with evenly cooking of the meat.
Generously season each side of the filets with salt and freshly ground black pepper, set aside.
Select a pan large enough to fit the fillets. Heat the pan over medium-high heat, for about 1 minute. Add 2 tablespoons of vegetable oil and heat until the oil is hot but not smoking, about 1 to 2 minutes.
Carefully add the seasoned filets to the pan. Cook over medium-high heat for about 5 to 6 minutes on each side, 10 to 12 minutes total.
Add the sprigs of rosemary and thyme to the pan, and 1 tablespoon of butter. When the butter is melted, spoon some of the butter over the steaks. Repeat this process for about 1 to 2 minutes. This will add more flavor to the steak.
Place fillets on a plate to rest, set aside. Do not discard the cooking pan! The fillets should have a nice caramelized brown color on the surface. The internal temperature should be around 120-125°F for medium-rare or 130-135°F for medium. Cook longer on each side for medium-well doneness. Allow the meat to rest for 15 minutes to achieve the final serving temperature.
Mushroom Pan Sauce
Using the same pan from cooking the steaks, begin to make the sauce. Remove the rosemary and thyme from the pan, discard.
Heat the pan over medium heat. Add the onions and sauté until translucent, about 4 minutes. If there are brown bits on the bottom of the pan from cooking the steak, try to scrape it off while you are cooking the vegetables, this will add amazing flavor as long as it’s not burnt! (If the cooking pan from the meat is not useable for the pan sauce, add 2 tablespoons of butter or oil to a fresh pan and proceed).
Add the sliced garlic and sauté for about 1 minute. Add the sliced mushrooms, sauté until tender, about 4 minutes. Add the bacon to the pan, saute for 1 minute.
Add the chicken stock to the pan. Turn the heat up to medium-high. Continuously stir the sauce until about half of the liquid has evaporated. It should be slightly thickened, but not runny.
Turn the heat down to low. Add the 1 tablespoon of butter and whisk. Season with salt and pepper to your liking. Turn off the heat and cover until ready to serve.
Broiled Lobster Tails
Preheat oven to broil. Line a small sheet pan with foil and set aside.
Place the lobster tails on a clean cutting board. With kitchen shears, cut the top of the lobster shells lengthwise. Slightly pull apart the shells to expose the meat. Remove any of the entrails. Gently rinse under cool water and dry.
Place the cleaned lobsters on the foil-lined baking sheet. Season with 1 to 2 tablespoons of melted butter (you can coat the outside of the shell with butter as well). Add about ⅛ teaspoon of the paprika evenly over the meat. Season with salt and pepper. Add a few slices of the garlic on top.
Place the tray on the middle rack of the oven. Broil lobster tails until lightly brown and shells turn a reddish color and the meat is opaque, about 4 to 6 minutes (add additional time for larger tails). Remove the lobster from the oven and check the meat for doneness before cooking longer.
If needed, reheat the steaks in the broiler for 1-2 minutes if the steak has cooled down, keep a close eye on them. Remove from the oven and set aside.
Reheat the mushroom pan sauce for a few minutes until hot.
On a plate, place the steak with the mushroom sauce on top. Add the lobster tail and lemon wedges. Serve with a side of melted butter if desired for the lobster.