In a large cast iron or stainless steel skillet, preheat about 1/2 inch oil to 350°F (177°C). In a medium bowl, combine 1/2 cup (65g) flour with cornstarch, 1/2 teaspoon kosher salt, 1/4 teaspoon ground black pepper, baking powder, and paprika and whisk to combine. Place remaining 1/2 cup flour in a shallow bowl.
Add crabs to plain flour and toss gently to coat. Add beer to flour/cornstarch mixture and whisk until a batter has just formed; it's okay if a few small lumps of dry flour remain.
Working with one at a time, lift a crab from flour and shake off excess. Dip in batter, turning to coat, then lift, allowing excess batter to drain back into bowl. Carefully lower crab into hot oil. Repeat with remaining crabs.
Cook, turning at least once, until batter is golden and crispy on both sides, about 3 minutes per side. Using a slotted fish spatula, transfer crabs to paper towels to drain and sprinkle immediately with salt.
Smear top and bottom of each bun with mayo, tartar sauce, or remoulade. Add shredded lettuce to each bottom bun, followed by a slice or two of tomato. Top each with a fried crab and close sandwiches. Serve right away.