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 so the bread lifts out easily.
Make the cinnamon sugar: In a small bowl, mix 1/3 cup sugar, 1 teaspoon cinnamon, and a pinch of salt. Set aside.
Combine dry ingredients: In a large bowl, whisk flour, 3/4 cup granulated sugar, 1/4 cup brown sugar, 2 teaspoons cinnamon, baking powder, baking soda, and salt until evenly blended.
Whisk the wet ingredients: In a separate bowl, whisk oil, yogurt, eggs, and vanilla until smooth and glossy.
Fold the batter: Pour the wet mixture into the dry ingredients. Stir gently with a spatula until a few streaks of flour remain.
Fold in the diced apples. The batter will be thick—this helps suspend the apples.
Layer with cinnamon sugar: Spread half the batter in the pan. Sprinkle half the cinnamon sugar evenly over it.
Spoon the remaining batter on top and smooth gently. Finish with the remaining cinnamon sugar.
Bake: Bake for 50–60 minutes, or until a toothpick inserted near the center comes out with just a few moist crumbs. If the top is browning too quickly, tent with foil for the last 10–15 minutes.
Optional finish: Right out of the oven, brush the top with melted butter to help the cinnamon sugar set into a crackly crust.
Cool and slice: Let the loaf cool in the pan for 15 minutes, then lift it out to a rack.
Cool completely before slicing to keep the crumb moist and intact.