Preheat your oven to 350 degrees and grease a 9×13-inch sheet pan with nonstick cooking spray.
In a large mixing bowl, whisk together the dry ingredients - flour, baking soda, kosher salt, cardamom, cinnamon, nutmeg, and ground cloves.
In a medium bowl, whisk together the wet ingredients - oil, granulated sugar, eggs, buttermilk, and vanilla extract. Stir in the shredded carrots and walnuts (if using).
Add the liquid ingredients to the dry ingredients and stir until just combined.
Pour batter evenly into the prepared sheet pan using a rubber spatula. You might have some batter leftover which is great to use to make some mini carrot cakes! Place on the middle rack in the oven and bake for 15 to 20 minutes or until a toothpick inserted in the center comes out clean. If the top starts to brown too quickly, you can loosely cover the top with aluminum foil or parchment paper hallway through.
Remove from the oven and let the cake cool on a wire rack for about 15 to 30 minutes. While the cake is cooling, make the ginger marshmallow frosting.
Use a stand mixer or hand mixer to beat the egg whites on medium speed with kosher salt until frothy. Gradually add the granulated sugar, beating until soft peaks form. Pour the corn syrup into a microwave safe bowl. Heat the syrup in the microwave until it boils. Once the syrup is boiling, remove from the microwave and pour in a thin stream over the egg white mixture.
Continue beating until stiff peaks form. Add in the vanilla extract and fresh ginger, and beat until glossy. Spread the frosting over the cake and garnish with shredded carrots and chopped walnuts if desired. Cut into slices and serve.