Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Stir oats, all-purpose flour, whole wheat flour, baking powder, salt, and baking soda together in a bowl.
Beat white sugar, brown sugar, and butter together in a large bowl using an electric mixer until fluffy. Beat in eggs, applesauce, and vanilla extract in that order. Stir in the oat-flour mixture until dough is just combined. Stir in chocolate chips.
Drop 1/4 cup of the dough onto the prepared baking sheet. Repeat with the remaining dough, flattening each cookie slightly.
Bake in the preheated oven until light brown at the edges, 12 to 15 minutes. Let cool on the baking sheet, 3 to 4 minutes. Transfer cookies to a wire rack to cool completely.