In a small bowl, combine the melted butter, olive oil, garlic, lemon juice, paprika, cayenne pepper, thyme, salt, and pepper. Mix well and set aside.
Using kitchen shears or scissors, cut the top of the lobster shell lengthwise down the center, but not all the way to the tail. Pry the shell apart slightly, keeping the fin end intact, lift the meat and lay it over the shell.
Brush the meat with the garlic sauce, making sure to completely cover all the meat.
Place the tails in a 9”x13” baking sheet, cover with a plastic wrap, and let them marinate in the fridge for 25-30 minutes.
Preheat the oven to broil, place the baking pan on the upper-middle rack, and broil the tails for 5-10 minutes (depending on their size) or until the flesh is opaque and firm.
Remove from the oven and serve immediately with your chosen sides.