BBQ Duck on Corn Cakes

Name: BBQ Duck on Corn Cakes
Ingredients: 1/2 cup all-purpose flour; 1/3 cup stone-ground cornmeal; 3/4 teaspoon baking powder; 1 teaspoon sugar; 1/4 teaspoon paprika; 1/2 teaspoon fine salt; 1 ear corn, shucked; 1/2 cup milk; 2 tablespoons plus 2 teaspoons unsalted butter, melted; 1 large egg, separated; 2 to 3 duck confit legs, skinned and meat shredded (recommended: D'Artagnan); About 1 cup KC Style BBQ Sauce, recipe follows; 2 tablespoons neutral tasting oil, such as grapeseed or vegetable; 6 cloves garlic, smashed; 2 tablespoons tomato paste; 1 slightly heaping tablespoon chili powder; 1 tablespoon paprika; 1 teaspoon crushed red pepper flakes; 1/4 teaspoon ground allspic; Pinch ground cloves; 2 cups ketchup; 2 cups water; 1/2 cup cider vinegar; 1/4 cup dark molasses; 1/4 cup firmly packed dark brown sugar; 1 tablespoon kosher salt; 1 tablespoon soy sauce; 1 tablespoon Worcestershire sauce; 2 teaspoons English-style dry mustard; 1 teaspoon freshly ground black pepper