Preheat your oven to 350°F (175°C). Butter a 9x5-inch loaf pan. Line it with parchment paper and set aside.
In a medium bowl, whisk the flour, baking soda, baking powder, ginger, cinnamon, and salt. Set aside.
In a separate large bowl, whisk together the eggs, vanilla extract and both sugars until smooth and creamy. Slowly mix in the melted butter.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the grated carrots until evenly distributed throughout the batter.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake in the preheated oven for 45-55 minutes, or until a toothpick inserted into the center comes out clean.
Remove the loaf from the oven and allow it to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
Make the cream cheese frosting. In a small bowl, beat the softened cream cheese and butter until smooth.
Add the powdered sugar and vanilla extract, and beat until well combined.
Spread the frosting over the cooled carrot cake loaf. Slice, serve, and enjoy!