Combine the flour, granulated sugar, brown sugar, cinnamon, baking powder, and salt in a medium bowl. Stir well and set aside.

In a large mixing bowl, whisk together the eggs, buttermilk, applesauce, vegetable oil, and vanilla extract until the mixture is smooth.

Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Fold in the diced apples, being careful not to overmix. Cover the bowl with a towel and let the batter rest for 15 minutes.

Preheat the oven to 425°F (220°C). Line a 12-cup muffin tin with 6 liners, spacing them out in every other cup to give the muffins room to rise. Fill each liner to the top with batter, smoothing the tops with a butter knife if needed.

Bake the muffins at 425°F (220°C) for 7 minutes. Without opening the oven door, lower the temperature to 350°F (175°C) and continue baking for 16-21 minutes, or until a toothpick inserted into the center comes out clean. Allow the muffins to cool in the pan for 15 minutes before transferring them to a wire rack.

Repeat the baking process with the remaining batter, making sure to preheat the oven back to 425°F (220°C) before starting.

To make the topping, melt the butter in a small dish. In a separate bowl, mix the cinnamon and sugar. Brush the tops of the cooled muffins with the melted butter, then dip them into the cinnamon-sugar mixture to coat evenly. Enjoy!