Preheat oven to 350°F. Grease and flour an 8 x 5 inch loaf pan or line it with parchment paper. Set aside.
In a small bowl, mix together brown sugar and cinnamon. Set aside.
In a large mixing bowl, whisk together eggs and granulated sugar.
Add melted butter and vanilla extract to the egg mixture, whisking until fully combined.
Gently stir in all-purpose flour, baking powder, baking soda, and salt until just combined. The batter will be very thick. Fold in the diced apples.
Pour half of the batter into the prepared loaf pan. Sprinkle about three-quarters of the brown sugar mixture over the batter.
Carefully spread the remaining batter on top of the brown sugar mixture. Sprinkle the remaining brown sugar mixture on top and gently swirl it into the top layer using a knife or spoon.
Bake for 35 to 45 minutes or until the top is lightly golden and a toothpick inserted in the center comes out clean or with a few moist crumbs. If the bread is browning too quickly, cover it with foil for the last 10 to 15 minutes.
Allow the bread to cool completely before slicing and serving.