1Stir the mayonnaise, mustard, relish, Old Bay, the juice of half the lemon, and half the parsley in a small bowl. Add a pinch of pepper and refrigerate until serving. Cut the remaining lemon half into wedges.
2Take the crab cakes out of the package and pat them dry with a paper towel so they brown well. They are already shaped and seasoned, so no chilling is needed.
3Heat the butter and vegetable oil in a large skillet over medium heat until the butter foams.
4Lay in the crab cakes without crowding them, working in batches if needed. Cook without moving them for 4 minutes, until the underside is deep golden.
5Flip carefully with a wide spatula and cook 3 to 4 minutes more, until browned and hot through (165°F in the center).
6Serve right away with the sauce, lemon wedges, and the remaining parsley sprinkled on top.
7Let the leftover fat in the skillet cool completely in the pan. Spoon it into a sealed container and discard it with the trash. Never pour it down the drain, since it hardens in the pipe.