Crisp, golden crab cakes are delicious on their own, but topped with fried oysters and a fresh tomato-cucumber relish, they're downright spectacular.
Pulse bread in a food processor until finely chopped. (You should have 1/2 cup.)
In a large bowl, toss together celery, pepperoncini, parsley, breadcrumbs, and crabmeat to combine. Add mayonnaise, Dijon, 1/4 teaspoon cayenne, egg, and 3/4 teaspoon salt; gently stir to combine. Form mixture into eight 2 1/2-inch-diameter patties (about 1/3 cup each). Refrigerate at least 15 minutes or, covered, up to 1 day.
In a shallow bowl, whisk together flour, pinch of cayenne, and a pinch of salt. In a large, heavy-bottomed skillet (preferably cast iron), heat 1/2 inch oil over medium-high. Add a pinch of flour mixture; if it sizzles, oil is ready. Working in batches, gently add crab cakes to oil, reduce heat to medium, and fry, flipping once, until golden and crisp, about 4 minutes a side. Drain on paper towels; sprinkle with salt. Strain oil into a small saucepan until you have 1 inch (adding more oil, if necessary) and heat over medium-high to 350 degrees.
Pat oysters dry. Dredge in flour mixture, shaking off excess. Fry until golden and crisp, 2 to 3 minutes. Transfer to paper towels. To serve, place a few lettuce leaves on each plate; top with crab cakes, a few fried oysters, and relish. Squeeze lemon wedges over top if desired.
Use a flexible spatula for easy flipping when frying.