Heat 1 tablespoon vegetable oil in a skillet over medium heat; cook and stir leeks until slightly browned, about 5 minutes.

Stir beer, milk, butter, and egg together in a bowl. Whisk whole wheat flour, all-purpose flour, baking powder, salt, sugar, black pepper, basil, and thyme into beer mixture until batter is smooth. Fold corn, Cheddar cheese, and leeks into batter.

Heat about 2 tablespoons vegetable oil in a large pan over medium heat. Drop large spoonfuls batter into the hot oil and fry until golden, 3 to 5 minutes. Add 2 more tablespoons oil to skillet and flip fritters; fry until other side is golden, 3 to 5 minutes. Remove fritters with a slotted spoon and place on a paper towel-lined plate. Repeat with remaining batter and oil.