Preheat the oven to 200°F. Heat 3 tablespoons of the clarified butter in a heavy large saute pan over medium-high heat. Sprinkle the crabs with fleur de sel and pepper. Dredge 4 of the crabs in the flour; shake off the excess flour. Add the coated crabs to the clarified butter and cook until golden brown and crisp, about 2 minutes per side. Transfer the crabs to a baking sheet and keep warm in the oven. Wipe out the saute pan. Repeat with the remaining 3 tablespoons clarified butter and 4 crabs.

Add the unsalted butter to the saute pan. Stir over medium-low heat until the butter melts and is golden brown, about 2 minutes. Whisk in the lemon juice, ginger, vinegar, capers, parsley, and tomato. Season the sauce to taste with fleur de sel and pepper.

Place 2 crabs on each of 4 plates. Spoon the sauce over the crabs and serve immediately.