Mix buttermilk and oats in a large bowl; allow to rest about 5 minutes. Stir flour, cornmeal, baking powder, sugar, baking soda, and salt into oat mixture. Add eggs and vegetable oil; mix until just combined.
Heat a lightly oiled griddle over medium-high heat. Drop batter by large spoonfuls onto the griddle; cook until bubbles form and the edges are dry, about 3 minutes. Flip and cook until browned on the other side, about 3 minutes more. Repeat with remaining batter.