Prep the pan and oven. Heat the oven to 350°F (175°C).
Grease a 9x5-inch loaf pan and line it with a parchment sling for easy removal.
Mix the cinnamon-sugar swirl. In a small bowl, combine 1/3 cup granulated sugar with 1 tablespoon ground cinnamon. Set aside.
Whisk the dry ingredients. In a large bowl, whisk 2 cups all-purpose flour, 1 teaspoon baking powder, 1/2 teaspoon baking soda, 1/2 teaspoon kosher salt, 1 teaspoon ground cinnamon, and a pinch of nutmeg if using.
Whisk the wet ingredients. In a separate bowl, whisk 2 large eggs, 1/2 cup granulated sugar, 1/2 cup packed light brown sugar, 1/2 cup oil, 1/2 cup unsweetened applesauce, 1/2 cup buttermilk, and 2 teaspoons vanilla extract until smooth.
Prep the apples. Peel and core 2 medium apples. Chop them into small, even pieces (about 1/4-inch).
You’ll want roughly 1.5 to 2 cups total. Pat dry with a paper towel to remove excess moisture.
Combine wet and dry. Pour the wet ingredients into the dry. Stir with a spatula until just combined.
The batter should be thick but pourable. Do not overmix.
Fold in apples. Gently fold in the chopped apples until evenly distributed.
Layer with the swirl. Spoon half the batter into the prepared pan. Sprinkle on half the cinnamon-sugar mixture.
Add the remaining batter, then top with the rest of the cinnamon-sugar. Use a butter knife to make a few gentle figure-8 swirls.
Bake. Bake for 55–65 minutes, or until a tester inserted in the center comes out clean or with a few moist crumbs. If the top browns too quickly, tent loosely with foil for the last 15 minutes.
Cool. Let the loaf cool in the pan for 15 minutes, then lift it out using the parchment and cool completely on a rack.
For a soft sheen, brush the warm top with 1 tablespoon melted butter (optional).
Slice and serve. Use a serrated knife for neat slices. Serve plain, with butter, or toasted the next day.