Preheat oven to 300 F.
Line a 9x5-inch loaf pan with parchment paper, leaving overhang on the long sides. Lightly grease remaining short sides of pan. Set aside.
Prepare the streusal by combining white flour, granulated sugar, brown sugar, and cinnamon. Pour in melted butter. Blend together with a fork or spoon, breaking up larger pieces. Set aside.
Finely shred carrots, chopping as desired to break up any larger pieces.
In a large bowl or stand mixer, combine vegetable oil with applesauce. Mix in sugar, followed by eggs and vanilla. Mix until fully combined. Add cinnamon, salt, and baking powder, mixing until just combined. Add carrots, followed by flour, mixing until no streaks remain. Pour batter into prepared loaf pan.
Sprinkle streusel topping over batter.
Bake for 55-60 minutes or until a toothpick inserted in the centre comes out clean. Cool completely in pan.
Carefully remove loaf by pulling up and outwards on parchment paper, Remove parchment paper and slice into desired thickness.
Store in an airtight container for up to several days.