Preheat oven to 400ºF. Line an 11-by-17-inch rimmed baking sheet with parchment paper.
Gently stir together the flour, oats, baking powder, cinnamon, baking soda, and salt in a medium bowl.
Add the eggs, milk, butter, vanilla, and shredded apple. Stir to combine.
Scrape the batter onto the parchment paper, smoothing into an even layer with a spatula just about to the edges. You want it to be about 1/2 inch thick all around.
Bake until the pancake is lightly golden and springs back in the center when poked, 18 to 20 minutes.
Serve warm.
Video
Notes
To store leftovers, let pancakes cool and store in an airtight container in the fridge for 3-5 days. Warm for 15-30 seconds in the microwave and serve warm. You can also freeze for up to 3 months in a zip-top freezer bag.
Gluten-free: Use cup-for-cup gluten-free flour instead of the whole wheat and certified gluten-free rolled oats.
Dairy-free: Use plain nondairy milk and coconut oil or canola oil for the butter.
Egg-free: Use a favorite store-bought egg substitute like the one from Bob's Red Mill.
Top with additional applesauce, apple butter, nut butter, or maple syrup as desired.