Preheat your oven to 350°F (175°C). Grease a 13x9-inch (33 × 23 cm)rectangular pan and line it with an overhang of baking paper on all four sides for easy removal.
Grate the carrots using the fine or medium side of a grater and lightly squeeze out excess moisture to prevent a dense cake.
In a large bowl, whisk together milk, oil, vanilla, light brown sugar, and cane/castor sugar until smooth.
In a separate bowl, combine the flour, baking powder, baking soda, cinnamon, and salt. Add the dry ingredients to the wet and mix until just combined without any lumps.
Gently fold in the grated carrots.
Pour the batter into the prepared pan and spread it in even layer. Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean. Let the cake col completely before frosting.