How to Make It
Preheat oven to 325°F. Grease and flour 2 (9-inch) round cake pans. Whisk together flour, sugar, baking powder, and salt in a medium bowl. Whisk together egg yolks, oil, 1/4 cup water, and vanilla in a separate bowl. Set aside.
Place egg whites in bowl of a heavy-duty stand mixer fitted with the whisk attachment. Beat on medium speed until foamy, about 30 seconds. Add cream of tartar, and beat on medium speed until stiff peaks form, 2 to 3 minutes. Reduce speed to low. Gradually add flour mixture to egg whites alternately with yolk mixture, beginning and ending with flour mixture, beating just until incorporated after each addition. Pour batter into prepared pans, and bake in preheated oven until a wooden pick inserted in center comes out clean, 25 to 28 minutes. Cool cakes in pans on wire racks 30 minutes. Remove cakes from pans to racks, and cool completely, about 30 minutes.
Combine cardamom pods, allspice berries, and star anise in a small skillet. Cook over medium-low, stirring often, until fragrant, about 1 minute and 30 seconds. Add ginger and fennel. Cook, stirring constantly, until mixture just begins to smoke, about 30 seconds. Transfer spices to a mortar and pestle or a spice grinder, and grind until very finely ground.
Scrape cream from top of coconut milk, and transfer to a small bowl; cover and chill. Combine coconut milk liquid, whole milk, cinnamon sticks, and ground spices in a medium saucepan. Bring to a simmer over medium, stirring occasionally. Simmer, stirring often, until flavors are infused, about 5 minutes. Add tea, and cook, stirring often, until mixture is fragrant, about 2 minutes. Pour mixture through a fine wire-mesh strainer into a bowl; discard solids. Whisk condensed milk into mixture until combined.
Using a serrated knife, cut a thin slice (about 1/8 inch) off the top of each cake layer, and discard. Place cake layers, cut sides up, on a rimmed baking sheet. Pierce tops of cakes all over with a fork. Spoon warm milk mixture over cakes, allowing liquid to absorb. Let cakes stand at room temperature 30 to 45 minutes, occasionally spooning milk mixture runoff over cakes. Carefully flip cakes, and continue spooning milk mixture runoff over cakes until most of liquid is absorbed, 30 to 45 minutes. (There may be about 1 cup milk mixture that does not soak in.) Cover and chill cake layers 1 hour.
Combine heavy cream and reserved coconut cream in bowl of a stand mixer fitted with the whisk attachment. With mixer running on medium-high speed, gradually add sugar. Beat until stiff peaks form, 2 to 3 minutes.
Carefully transfer 1 cake layer to a serving platter. Spread half of whipped cream mixture over top of bottom layer; top with half of strawberries and second cake layer. Spread top with remaining whipped cream mixture. Garnish with remaining strawberries. Chill 1 hour before serving.