On a piece of waxed paper or paper plate, mix together the flour, paprika, parsley, salt and pepper. Pat the crabs dry with a paper towel. Coat with the flour mixture and remove excess.

Heat the oil and butter in a large skillet over medium high heat. Add the crabs, in batches if necessary, and sauté until nicely browned, about 3 minutes per side. (Soft shell crabs contain a lot of moisture and might "spit" while browning, so be careful.) Drizzle each crab with a little lemon juice and sprinkle with salt. Serve immediately, with the remoulade on the side.