In a medium skillet over medium heat, melt 2 tablespoons butter. Add diced apples, brown sugar, cinnamon, and a pinch of salt. Stir to coat the apples.
Cook for 3-5 minutes, stirring occasionally, until apples are tender and syrupy. Turn off heat and set aside.
In a medium bowl, whisk together flour, brown sugar, baking powder, cinnamon, and salt until well combined.
In a large bowl, whisk together milk, melted butter, eggs, vanilla extract, and salt until frothy.
Gently fold the dry ingredients into the wet ingredients using a flexible spatula. Mix just until no dry flour remains. Do not overmix - lumps are okay.
Fold in the grated apple gently. Let the batter rest for 5 minutes to thicken.
Heat a nonstick or cast-iron skillet over medium heat for 2 minutes. Add 1 teaspoon oil and swirl to coat.
Pour 1/4 cup batter per pancake into the skillet, making 3-4 pancakes depending on skillet size. Leave space between them.
Cook for 2-3 minutes until bubbles form on the surface and edges look set. The bottoms should be deep golden-brown.
Flip gently with a wide spatula and cook the second side for 2-3 minutes until golden-brown.
Transfer to a plate and keep warm in a 250°F oven if making multiple batches. Add 1 teaspoon oil before each new batch.
Serve warm pancakes topped with butter, the caramelized apple topping, and maple syrup if desired.