Preheat the oven to 340°F (170°C). Grease and line four 8-inch (20 cm) round cake pans with parchment paper. In a stand mixer, beat butter, oil, and sugar until pale and fluffy. Add eggs one at a time, mixing well after each addition. Add sifted flour, salt, and coconut, mixing on low speed. Slowly pour in coconut cream and vanilla extract until just combined.
Divide the batter evenly between the prepared pans and use an offset spatula to smooth the tops. Bake for 20–25 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool in their pans for 10 minutes, then carefully turn them out onto a wire rack to cool completely. Once cooled, use a cake leveler to trim the caramelized top layer of each sponge, ensuring even and level layers for stable assembly.
Combine egg whites and sugar in a heatproof bowl over a bain-marie. Whisk constantly until the mixture reaches 160°F (70°C) and the sugar is dissolved.
Transfer the bowl to a stand mixer with the whisk attachment. Whip on high speed until stiff, glossy peaks form and the bowl feels cool to the touch.
Reduce the mixer speed to medium. Add softened butter one cube at a time, allowing each cube to fully incorporate before adding the next. Continue mixing until smooth and silky.
On low speed, mix in mascarpone cheese, almond extract, coconut milk, and salt until smooth and evenly combined.
Set aside 10–15% of the buttercream for decoration. Spread a thin layer of buttercream on the cake stand to secure the first sponge layer. Layer the sponges with ½ inch (1 cm) thick layers of buttercream between each. Apply a thin crumb coat, smooth it out, and refrigerate for 20 minutes.
Spread the remaining buttercream evenly over the top and sides of the cake. Use an offset spatula and bench scraper to achieve a smooth finish.
Tint the reserved buttercream green and use a piping bag with a star tip to create tree designs. Decorate with sprinkles and a star anise topper. Chill briefly to set the design.
Let the cake sit at room temperature for 20–30 minutes before slicing. Serve each slice with a warm drink like almond latte or coconut hot chocolate.