Stir together first 7 ingredients, 1 teaspoon of the salt, and 1⁄2 teaspoon of the pepper in a bowl; set aside.

Using a sharp pair of kitchen shears, snip off mouth and eyes of crabs; squeeze out gooey matter where cut was made. Carefully raise top shell on far left of crab. Use shears to cut away feathery-looking gills; repeat procedure on right side of crab. Turn crab over, and remove tough flap from stomach.

Stir together flour and remaining 1⁄2 teaspoon each salt and pepper. Dredge crabs in flour mixture, shaking off excess. Melt 2 tablespoons butter with 2 tablespoons oil in a large skillet over medium-high until hot. Add 3 prepared crabs; cook until golden brown and aromatic, 4 to 5 minutes per side. Place crabs on paper towels to drain and cool. Repeat with remaining butter, oil, and prepared crabs.

Divide sauce, fried crabs, lettuce, and tomatoes evenly among potato rolls, and serve immediately.