Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan and dust with flour.

Place apples in a bowl and sprinkle with vinegar. Set aside.

Whisk white sugar, brown sugar, eggs, and vanilla extract together in a large bowl until well combined and pale brown. Add melted butter and whisk until smooth. Add flour, cocoa powder, baking powder, cinnamon, nutmeg, and salt. Whisk until brownie batter is well combined.

Sprinkle 2 tablespoons flour over apples in the bowl and toss to coat. Fold floured apples and chocolate chips into the brownie batter; batter will be thick. Spread batter evenly into the prepared pan.

Bake in the preheated oven until top is no longer shiny and a toothpick inserted in the center comes out clean, about 30 minutes, but check after 25 minutes and do not overbake.