Preheat the oven to 350°F. Lightly butter and line a 8 inch square cake pan with parchment paper. In a bowl, whisk together the flour, baking soda, salt, cinnamon, and ginger. Set aside.
Whisk the oil and sugars together in a bowl until well blended. Whisk in the eggs, one at a time until incorporated.
Stir in the flour mixture until just blended, then stir in the carrots and grated ginger.
Pour the batter into the prepared pans and bake for 25-30 minutes or until a tester in the middle of the cake comes out clean. Cool in the pan for 15 minutes, then turn out onto a cooling rack, peel off the parchment paper and cool completely.
Make the frosting by whip together all the frosting ingredients in a stand mixer until full and fluffy. Frost your cake and enjoy!
