Whisk flour, milk, eggs, 1 tablespoon oil, baking powder, salt and pepper in a medium bowl until smooth. Stir in corn and basil.
Brush a large nonstick skillet lightly with some of the remaining 1 tablespoon oil; heat over medium heat until hot (but not smoking). Cook 4 cakes at a time, using about 1/4 cup batter for each, making them about 3 inches wide. Cook until the edges are dry, about 2 minutes. Flip and cook until golden brown on the other side, 1 to 3 minutes more. Repeat with the remaining oil and batter, making 10 cakes total. Reduce the heat as necessary to prevent burning.