Melt White Chocolate: Place white chocolate over a double boiler, stirring until melted. Let it cool to room temperature.
Prep: Grease an 8.7x4.6-inch bundt pan with butter or oil. Dust with brown sugar or coconut sugar if desired. Preheat the oven to 170°C/325°F.
Cream Butter and Sugar: In a large bowl, beat softened butter and granulated sugar until smooth and fluffy. Add 2 tablespoons of coconut cream and beat until creamy.
Add Eggs and Flavoring: Add eggs, one at a time, beating after each addition. Stir in the melted white chocolate and vanilla extract.
Prepare Dry Ingredients: Sift together all-purpose flour, baking powder, baking soda, and salt in a separate bowl.
Prepare Wet Ingredients: Mix coconut milk with yogurt in another small bowl.
Combine Mixtures: Alternately add the dry ingredients and the coconut milk-yogurt mixture to the butter-sugar mixture, starting and ending with dry ingredients. Beat gently after each addition and finish mixing with a spatula.
Bake: Pour the batter into the prepared pan and tap it gently on the counter to release air bubbles. Bake in a preheated oven at 170°C/325°F for 65-75 minutes. Cover with foil if browning too much.
Cool: Let the cake cool in the pan for 5-8 minutes before transferring it to a wire rack to cool completely.
Prepare Frosting: Beat cream cheese and butter until creamy. Mix in coconut cream and powdered sugar. Chill for 1 hour.
Frost and Decorate: Spread the frosting over the cooled cake and cover with desiccated or fresh coconut.