Make the compound butter: in a small bowl use a fork to combine 4 tablespoons unsalted butter (softened), 2 teaspoons minced shallot, 1 minced garlic clove, and 2 teaspoons minced fresh parsley.

Transfer the butter mixture to a sheet of wax paper or plastic wrap. Form it into a 1½-inch-thick log, roll tightly, freeze 10 minutes to firm, then refrigerate until ready to use.

Preheat the oven to 375°F and position a rack in the center. Line a baking sheet with aluminum foil and spray with nonstick spray; set the sheet aside.

Prepare the lobster tails: using kitchen shears, carefully split the top shells of the 2 lobster tails lengthwise. Insert an upside-down teaspoon between the underside of each shell and the meat to loosen it, lift the meat up, and rest the meat on top of the shell. Place the lobster tails on the prepared baking sheet.

Drizzle the lobster tails with the 2 tablespoons fresh lemon juice, dividing it evenly between the two tails.

Remove the compound butter log from the refrigerator and slice it into four equal pats. For each lobster tail, take one pat, cut that pat in half, and arrange the two halves on top of the lobster meat. Reserve the remaining two pats for the steaks. (If the butter is too soft to slice, chill briefly until firm enough to cut.)

Prepare the steaks: pat the steaks dry, drizzle them with 1 tablespoon of the olive oil, and season both sides evenly with 2 teaspoons kosher salt and 1½ teaspoons black pepper.

Heat the remaining 1 tablespoon olive oil in a cast-iron skillet over medium-high heat until shimmering. Add the steaks and sear 1–2 minutes per side.

Immediately transfer the skillet with the seared steaks to the preheated oven and at the same time put the baking sheet with the lobster tails into the oven. Cook the steaks 4–8 minutes in the oven, until they reach your desired doneness (use a thermometer: medium-rare 125–130°F; medium 135°F; medium-well 145°F). Cook the lobster tails 6–8 minutes, until the meat is firm and opaque.

Remove the steaks from the oven when they reach the desired temperature and transfer them to a plate. Top each filet with one reserved pat of compound butter and let the steaks rest for 5 minutes while the lobster finishes cooking.

When the lobster meat is firm and opaque and the butter on top has melted slightly, remove the baking sheet from the oven. Arrange each filet and lobster tail on serving plates, garnish with lemon wedges, and serve.