Rinse crabs and pat them dry with absorbent paper. Set on a tray and season with kosher salt. Place flour and half the cayenne into a shallow bowl and stir together to combine. One at a time, press crabs into the flour, turning to coat both sides. Tap each crab as you’ve floured it to release any excess and set onto a plate.

Pour a thin slick of olive oil to coat a cast iron skillet, warmed over medium-high heat. Once the oil shimmers, turn heat to medium and place 2 crabs in to cook. Sear for 2 minutes on the first side, turn them over, and cook for another minute until browned and crispy at the edges. Transfer first batch to absorbent paper placed on a wire rack as you sear the second batch.

Halve avocados and discard pits. Scoop flesh into a bowl and coarsely mash with a fork. Add garlic, chili powder, lime juice, and salt to taste and stir to combine. Taste and adjust seasoning as needed.

Arrange elements on a platter in piles: the crabs, guacamole, corn kernels, and lime cheeks. Scatter with shaved jalapeño and parsley, lightly dust with remaining cayenne, and sprinkle all with flake salt.