Preheat oven to 350°F and grease or line a 9x5-inch loaf pan.
In a large bowl, whisk sugar, coconut oil, eggs, vanilla, and apple cider until smooth.
In another bowl, whisk together flour, baking powder, baking soda, cinnamon, and nutmeg.
Gently fold dry ingredients into the wet mixture until just combined. Stir in oats, then fold in diced apples.
Mix the topping ingredients (oats, brown sugar, butter) until crumbly.
Pour batter into loaf pan, sprinkle with topping, and bake 50–60 minutes, or until a toothpick comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.