Preheat your oven to 350°F and line a 9-inch round cake pan (or 8x8 square pan) with parchment paper. While the oven heats, finely mince the ginger into 1/4-inch pieces, shred the carrot using the small holes of a box grater, chop the walnuts into bite-sized pieces, and zest the orange and lime. Sift the 1 cup of icing sugar for the final glaze to remove any lumps—this ensures a smooth, lump-free glaze later.

While your oven finishes preheating, chop the white chocolate into small pieces and combine it with the unsalted butter in a heatproof bowl. Melt over a double boiler or in 30-second microwave bursts, stirring between bursts until completely smooth—I find Ghirardelli chocolate melts beautifully without seizing. Set aside to cool for 2-3 minutes. Simultaneously, whisk together the flour, cinnamon, allspice, and nutmeg in a separate bowl to combine the spices evenly throughout.

In a large mixing bowl, beat the eggs and sugar together for 2 minutes until pale and slightly fluffy—this aerates the batter for a lighter crumb. Pour the cooled chocolate-butter mixture into the eggs and mix until fully combined. Add the dry ingredient mixture from Step 2 and fold gently until just combined, being careful not to overmix. Fold in the carrot, walnuts, ginger, and orange zest from Step 1 until evenly distributed throughout the batter.

Pour the batter into your prepared pan and smooth the top with a spatula. Bake for 35-40 minutes until a toothpick inserted into the center comes out with just a few moist crumbs—the cake will continue to set as it cools. The top should look set and slightly golden. Remove from the oven and let cool completely in the pan, about 30-40 minutes, before moving on to glazing.

While the cake cools, prepare the first glaze by whisking together the 0.7 cup icing sugar and 2 tablespoons of lime juice until smooth and pourable. Once the cake has cooled completely, pour this glaze over the top, letting it drip down the sides naturally. Allow this first glaze to set for 45 minutes at room temperature—the acidity of the lime juice will add brightness to the white chocolate cake.

After 45 minutes, prepare the second glaze by whisking together the sifted icing sugar from Step 1 with the remaining 1 tablespoon of lime juice until you reach a smooth, spreadable consistency. Gently pour or spread this second glaze over the first layer, working quickly so it sets smoothly. Immediately sprinkle the reserved orange and lime zests over the top for brightness and color. Let the cake rest for 1 hour before serving to allow the glazes to fully set—this helps the slices cut cleanly.