How to Make It
In a spice mill or clean coffee grinder, grind the oatmeal to a fine powder. Transfer the oatmeal to a large, shallow bowl and whisk in the flour. Season the mixture generously with salt and pepper. In another large, shallow bowl, beat the egg with the buttermilk.
Line a baking sheet with wax paper. Dip 1 crab at a time in the buttermilk mixture and shake off any excess, then dredge it thoroughly in the oatmeal flour to make a thin coating. Transfer the crab to the prepared baking sheet. Repeat with the remaining crabs.
In each of 2 large skillets, melt 2 tablespoons of the butter in 4 tablespoons of the oil over moderately high heat. Fry 4 crabs in each skillet until browned and crisp on the bottom, about 3 minutes. Turn the crabs and fry until just cooked through, 1 to 2 minutes longer. Using a slotted spatula, transfer 2 crabs to each plate.
Wipe out 1 of the skillets. Add the remaining 6 tablespoons of butter and cook over moderately high heat until it starts to brown, about 3 minutes. Add the capers and cook until they start sizzling and open into flowers, about 1 minute. Add the lemon juice and swirl to blend with the butter. Drizzle the brown butter sauce over the crabs and around the plates. Sprinkle the parsley over the crabs and serve at once.
Shaved fennel and pea shoot salad with lemon vinaigrette.