Blend the oats in a food processor until they resemble fine flour.
Whisk oat flour, all-purpose flour, baking powder, baking soda, cinnamon, nutmeg, salt, and brown sugar in a large bowl.
In a separate bowl, whisk milk, yogurt, eggs, vanilla, and melted butter until smooth.
Toss the grated apple with lemon juice to prevent browning.
Pour the wet mixture into the dry ingredients and stir just until combined. Fold in the apple. Let the batter rest 5 minutes to hydrate.
Heat a nonstick skillet or griddle over medium heat and lightly butter the surface.
Scoop 1/4-cup portions of batter onto the skillet. Cook until bubbles form and edges look set, 2–3 minutes. Flip and cook 1–2 minutes more.
Hold pancakes warm and repeat with remaining batter. Serve with maple syrup and extra apple if desired.