Preheat the oven to 350°F. Grease an 8 ½ x 4 ½-inch loaf pan and line the bottom with parchment paper.
Use a stand mixer with the paddle attachment or hand beaters to beat the eggs and granulated sugar together until light and creamy, about 2 minutes. Add the melted butter, milk, and vanilla, and mix until evenly combined.
In a small bowl, mix together the flour, salt, and baking powder. Gradually add this to the wet ingredients and mix on low speed until combined. Stir in the diced apples.
Mix brown sugar and cinnamon in a small bowl.
Add ½ of the batter into the pan, then sprinkle ½ of the cinnamon-sugar mixture on top. Add the rest of the batter and sprinkle with the remaining cinnamon-sugar mixture.
To create the swirl, insert a butter knife in the batter and drag the knife through the batter in a zigzag motion. Do this only once.
Bake for 50-55 minutes or until a toothpick comes out clean (a few crumbs are ok but there should be no visible streaks of batter). Let the loaf cool in the pan for 10 minutes, then run a knife along the edges to remove the bread. Finish cooling on a wire rack, then slice and enjoy!