Preheat oven to 350°F (180°C). Grease a 9x5-inch (23x13 cm) loaf pan with butter.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a separate bowl, whisk together the sugars, yogurt, oil, eggs, and vanilla until fully combined.
Add the wet ingredients to the dry ingredients and mix until just combined.
Fold in the diced apples.
Pour the batter into the prepared loaf pan and bake for 40-45 minutes, or until a toothpick inserted into the center of the loaf comes out clean.
Let cool in the pan for 10 minutes, then remove and cool completely on a wire rack.