In a large bowl, whisk together the Greek yogurt, eggs, brown sugar, and vanilla.
In a smaller bowl, mix together the oat flour and the baking powder.
Add the flour mixture and the milk, alternating into the egg mixture, starting and finishing with the flour mixture.
Heat up a frying pan on medium-high heat or heat up a griddle to 375F. Use non-stick spray or butter to grease the pan. Drop ⅓ cup of batter onto the preheated surface.
Cook the pancakes until bubble form and the bottom is golden. Flip and cook until golden on both sides. Remove from the pan and repeat with the rest of the batter.