Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together butter, 1 1/2 cups granulated sugar, and brown sugar until fluffy.
Add eggs and vanilla extract; beat until combined.
In a separate bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
Gradually add dry ingredients to the wet mixture and mix until combined.
Fold in chopped apples.
In a small bowl, mix remaining 1/2 cup sugar with 2 tsp cinnamon.
Scoop dough into balls and roll in cinnamon-sugar mixture.
Place on prepared baking sheet, spacing about 2 inches apart.
Bake for 12–14 minutes, or until edges are set and cookies are lightly golden.
Cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.