Combine egg yolks, minced garlic, Dijon mustard, and lime juice in a tall narrow jar or blender cup.

Insert a stick blender and blend on high for 10 seconds until pale and slightly thickened.

With the blender running, drizzle in the neutral oil in a thin, steady stream until the mixture emulsifies into a thick, glossy aioli.

Stir in lime zest, salt, and white pepper. Taste and adjust acid or salt as needed. Refrigerate until ready to serve.

Pat cleaned crabs completely dry on both sides with paper towels. Any surface moisture will steam the crust.

Whisk together flour, cornstarch, salt, black pepper, garlic powder, and smoked paprika in a shallow dish.

Dredge each crab in the flour mixture, pressing lightly to coat the top, legs, and underside. Shake off any excess.

Pour oil into a 12-inch cast iron or stainless skillet and heat over medium-high until it reaches 180 C / 355 F on an instant-read thermometer.

Carefully lower 2 crabs into the oil, top-side down. They will pop and splatter, so use long tongs and stand back slightly.

Fry for 3 to 4 minutes until the underside is deep golden and the legs are crisp. Flip and fry for 2 to 3 minutes more until the second side is golden.

Transfer to a wire rack. Repeat with the remaining 2 crabs, allowing the oil to return to temperature between batches.

Season each crab lightly with flaky salt the moment it comes off the heat.

Plate immediately with a generous spoonful of lime aioli on the side and a fresh lime wedge.