Preheat the oven to 200 degrees F. Set a wire rack on a baking sheet and place in the oven.
Whisk 1 3/4 cups flour, the sugar, baking powder, salt and nutmeg in a large bowl. In small bowl or liquid measuring cup, whisk the eggs with the milk and vanilla extract. Melt 3 tablespoons butter in a large well-seasoned cast-iron or non-stick skillet over medium heat.
Whisk the butter into the milk mixture.
Add the liquid ingredients to the dry mixture, and whisk just long enough to make a thick batter, (if there are a couple lumps that's okay).
Using a melon baller or an apple corer, peel and core the apples keeping them whole. Slice the apples crosswise to make 1/4-inch rounds. Put some flour on a plate and dredge the apple slices until lightly coated, shaking off any excess flour.
In the same skillet over medium to medium-low heat, place 3 apple slices about 3-inches apart in the skillet. Cook without turning until browned, about 3 minutes. Ladle about 2 tablespoons of the batter over each apple ring. Cook, until bubbles break the surface of the pancakes, and the undersides are golden brown, about 2 to 3 minutes.
Add a nut-sized bit of butter to the skillet, as needed, and flip the pancakes, cook until golden on the underside, about 1 minute more.
Serve immediately or transfer to oven to keep warm. Repeat with the remaining apples and batter.
