In a mixing bowl, combine the room temperature butter, minced garlic, lemon zest, thyme leaves, parsley, and a pinch of salt and pepper. Mix well until all ingredients are thoroughly combined. Set aside a few tablespoons for the lobster and refrigerate the rest for later.
Using kitchen shears, carefully cut the top shell of the lobster tails down the center. Gently pull the meat upwards to expose it while keeping it attached at the base. Season the lobster meat with salt, pepper, and a tablespoon of the herb butter.
Preheat your grill or grill pan over medium-high heat. Place the lobster tails shell side down and grill for about 5-6 minutes until the meat is opaque and cooked through. Baste with herb butter while grilling for extra flavor.
While the lobster is cooking, season the filet mignon generously with coarse sea salt and pepper. Heat a large skillet over medium-high heat and add the neutral oil. Once hot, sear the filet mignon for 4-5 minutes on each side for medium-rare doneness.
In the last minute of cooking, add the butter, smashed garlic, and fresh thyme to the skillet. Spoon the melted butter over the steak for additional flavor as it finishes cooking.
Once both the lobster and steak are cooked, remove them from the heat. Let the steak rest for a few minutes before slicing. Arrange the lobster and filet mignon on a serving platter alongside baby tomatoes and your choice of greens or potatoes. Drizzle any remaining herb butter over the top for an extra burst of flavor.
