In a large bowl, whisk together the oat flour, sugar, baking powder, and salt until well combined.
In another bowl, mix the milk, egg, melted butter, 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.
Pour 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 another 1-2 minutes until golden brown.
Repeat with the remaining batter, adjusting the heat as necessary to prevent burning.
Serve warm with your favorite toppings such as maple syrup, fresh fruit, or yogurt.