Whisk the flour, baking powder, cinnamon and salt together in a medium bowl.
Whisk the milk, sugar, vanilla and eggs together in a large bowl until the sugar dissolves. Melt 2 tablespoons of the butter in a medium nonstick or cast-iron skillet over medium heat. Let cool slightly, then whisk the butter into the egg mixture; reserve the skillet for cooking the pancakes. Whisk the flour mixture into the milk mixture until combined with a few lumps. Grate the apple on the large holes of a box grater and stir into the batter.
Melt 1 tablespoon of the remaining butter in the reserved skillet over medium heat. Drop 2 tablespoons of batter per pancake into the hot skillet. Cook until the surface of the batter forms bubbles and the edges are set, about 3 minutes. Flip the pancakes and continue to cook until puffed in the center, about 1 minute more. Transfer to a baking sheet and put in the oven to keep warm while making the rest of the pancakes. Cook the remaining batter, adding the remaining 1 tablespoon of butter as needed.
Serve the pancakes with butter and maple syrup or honey.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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