In a large bowl, combine eggs, sugar, buttermilk, vanilla, and melted (cooled) butter. Whisk until well blended.
Place a sieve over the bowl and add flour, baking powder, baking soda, cinnamon, and salt. Stir with a spoon, then sift the dry ingredients into the bowl. Whisk until almost fully combined.
Peel, core, and chop the apples into small cubes (about 1/3-1/2 inch or 1 cm). Fold the apples into the batter with a spatula until evenly distributed and the batter is just combined (avoid overmixing).
Heat a small amount of clarified butter (or a mix of butter and oil) in a non-stick pan over medium/medium-low heat. When the pan is hot and the butter is bubbling, scoop about 1/4 cup of batter per pancake into the pan (keep them small as they will puff up).
Optionally, cover the pan with a lid to speed up cooking.
Cook the pancakes until golden on the bottom and bubbles form on top.
Flip the pancakes using two silicone spatulas or one large flat spatula and cook until browned on the other side.