Filet Mignon with Lobster Tail and Creamy Sauce: A Luxurious, Restaurant-Quality Dish

Preheat your oven to 400°F (200°C).
Using kitchen shears, carefully cut the top of the lobster shell lengthwise, exposing the meat. Gently pull the meat out, keeping it attached at the base of the tail, and place it on top of the shell.
Brush the lobster meat with melted butter and sprinkle with lemon juice, paprika, salt, and pepper. Place the lobster tails on a baking sheet and bake for 12-15 minutes, or until the meat is opaque and tender.
Cook the Filet Mignon:

While the lobster is baking, heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat.
Season the filet mignon steaks with salt and pepper on both sides. Once the pan is hot, add the steaks and sear them for 3-4 minutes per side for medium-rare (adjust the time if you prefer a different level of doneness).
Add the minced garlic and the remaining tablespoon of butter to the pan, and cook for an additional 1-2 minutes, spooning the melted butter over the steaks. Remove the steaks from the skillet and let them rest for 5 minutes before serving.
Make the Creamy Sauce:

In the same skillet, add the chopped shallot and sauté for 2-3 minutes until soft and translucent.
Deglaze the pan with white wine, scraping up any browned bits left from the steaks. Let the wine reduce by half, about 2 minutes.
Add the chicken broth and Dijon mustard, stirring until the sauce is smooth.
Lower the heat and pour in the heavy cream. Let the sauce simmer gently for 5-7 minutes, or until it thickens to your desired consistency. Season with salt and pepper to taste.
Stir in 1 tablespoon of butter for added richness and a glossy finish. If desired, sprinkle with freshly chopped parsley.
Assemble and Serve:

To serve, place each filet mignon steak on a plate. Top with a lobster tail, and spoon the creamy sauce generously over both the steak and lobster. Garnish with more parsley if desired.
Serving and Storage Tips: