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1
Make cake: Preheat oven to 350u00b0. Grease 3 round cake pans (8 in. each). Line each with a circle of parchment paper and set aside.
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2
Mix cake flour, whole-wheat flour, baking soda, baking powder, salt, cinnamon, cardamom, and star anise in a large bowl; set aside.
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3
In bowl of a stand mixer fitted with paddle attachment, beat oil, eggs, coconut sugar, yogurt, orange juice, bourbon, and vanilla on medium speed until well blended. Add flour mixture; beat on low speed to blend, then on medium speed until smooth, scraping inside of bowl twice. Stir in orange zest and crystallized ginger, then squash.
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4
Divide batter among lined pans and spread level. Bake until a toothpick inserted in center comes out clean, 20 to 24 minutes.
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5
Turn cakes onto racks, remove parch-ment, and let cool completely, 1 to 1 1/2 hours.
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6
Make frosting: In bowl of a stand mixer fitted with paddle attachment, beat butter and cream cheese until very smooth. Add powdered sugar, bourbon, cardamom, salt, cinnamon, and ginger; beat on low speed to blend, then on high speed until smooth and fluffy, scraping inside of bowl once or twice.
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7
Set a cake layer rounded side down on a platter; spread top of it with 3/4 cup frosting. Repeat with second layer. Set top layer in place, rounded side up. Spread top and sides of cake with remaining frosting. Press coconut into sides, a small handful at a time.
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8
*Find coconut palm sugar in the baking aisle of well-stocked grocery stores. Toast coconut on a rimmed baking sheet in a 350u00b0 oven until light golden, stirring once, 4 to 5 minutes.
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9
Make ahead: Up to 1 day, chilled and loosely wrapped with plastic wrap.
