Blend the oats in a blender for 30–45 seconds, until they form a fine flour.
In a large bowl, whisk together the oat flour, all-purpose flour, sugar, baking powder and salt.
In another bowl, whisk the milk, eggs, melted butter and vanilla.
Pour the wet ingredients into the dry and stir until just combined. Let the batter rest for 5 minutes. If it’s too thick to pour, stir in another tablespoon or two of milk.
Heat a skillet or griddle over medium heat and grease it lightly. Pour ¼ cup of batter for each pancake.
Cook for 2–3 minutes, until bubbles form on the surface and the edges look set. Flip and cook for 1–2 minutes more, until golden. Repeat with the remaining batter.