Preheat oven to 350°F (175°C). Grease a 9x5 inch loaf pan and line with parchment paper sling.
In a small bowl, combine 3 tablespoons sugar with 1 1/2 teaspoons cinnamon for the swirl mixture.
Peel, core, and dice apples into 1/4 to 1/2 inch pieces. Measure 1 1/2 cups and set aside.
In a large bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg.
In a separate bowl, whisk eggs, granulated sugar, and brown sugar until pale and thickened. Add oil, sour cream, and vanilla, whisk until smooth.
Pour dry ingredients into wet and fold with a rubber spatula just until no flour streaks remain. Do not overmix.
Gently fold diced apples into the batter with 4 to 5 strokes until evenly distributed.
Spoon half the batter into the prepared pan and spread evenly. Sprinkle entire cinnamon sugar mixture over the top. Cover with remaining batter and gently spread.
Drag a butter knife through the batter in a figure-8 pattern 2 to 3 times for a marbled effect. Do not over-swirl.
Bake on center rack for 55 to 65 minutes until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Cool in pan for 15 minutes, then use parchment sling to lift onto a cooling rack. Cool for at least 30 to 45 minutes before slicing.
For the glaze: whisk powdered sugar, milk, and vanilla until smooth. Drizzle over cooled bread and let set for 10 minutes before serving.