In a saucepan, melt 2 tablespoons of butter over medium heat. Add minced garlic and sauté until fragrant. Stir in diced tomatoes and cook until softened. Add white wine and simmer until reduced by half. In a bowl, whisk together the egg yolk, lemon juice, Dijon mustard, cayenne pepper, salt, and black pepper. Slowly add the tomato mixture to the egg yolk mixture while whisking continuously until well combined. Set aside.

Prepare the Oysters

Preheat your grill or oven to high heat. In a bowl, combine the jumbo lump crab meat, chopped dill, and the remaining 2 tablespoons of melted butter. Season with salt and black pepper to taste.

Assemble the Oysters

Place shucked oysters on a grill-safe tray or directly on the grill. Spoon the crab mixture generously onto each oyster.

Grill the Oysters

Place the tray on the preheated grill and cover. Grill for about 5-7 minutes, or until the crab is heated through and the oysters are slightly charred.

Serve

Remove the oysters from the grill and drizzle with the prepared tomato Béarnaise. Garnish with additional dill if desired. Serve immediately.