Preheat your oven to 350°F (175°C). Grease two 9-inch round cake pans and line the bottoms with parchment if you like. If you use a 9x13 pan, grease it well.

In a large bowl, whisk together flour, granulated sugar, brown sugar, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger until even.

In a separate bowl, beat the eggs. Add the oil, yogurt, orange juice, orange zest, and vanilla. Mix well until smooth.

Pour the wet ingredients into the dry ingredients. Stir with a spatula or whisk until just combined. Do not overmix.

Fold in the grated carrots and chopped nuts gently until they spread through the batter. The batter will be thick but moist.

Divide the batter between the two prepared pans and smooth the tops. For a 9x13 pan, pour all batter in and spread evenly.

Bake for 25–30 minutes for round pans, or 35–40 minutes for a 9x13, or until a toothpick in the center comes out clean or with a few moist crumbs. Do not overbake.

Let the cakes cool in the pans for 10 minutes. Turn them out onto a cooling rack and let cool completely before frosting.

To make the frosting: beat the cream cheese and butter together until smooth. Add vanilla.

Slowly add powdered sugar until you reach a spreadable texture. If the frosting is too thick, add a splash of orange juice or milk.

Place one cake layer on your plate. Spread a layer of frosting. Add the second cake layer and frost the top and sides. Smooth or make small swirls with a spatula. Garnish with a few reserved chopped nuts or thin orange slices.