In a large mixing bowl, whisk together the oat flour, sugar, baking powder, and salt until well combined.
In a separate bowl, mix the milk, egg, melted butter (or oil), and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix; a few lumps are okay.
Preheat a non-stick skillet or griddle over medium heat. Lightly grease with butter or oil if necessary.
Pour about 1/4 cup of batter onto the skillet for each pancake. Cook until bubbles form on the surface, about 2-3 minutes. Flip and cook for an additional 1-2 minutes, or until golden brown.
Repeat with the remaining batter, adjusting the heat as needed to prevent burning.