Preheat oven to 350 degrees F (175 degrees C). Line a muffin tin with paper liners.
Combine 2 1/3 cups plus 1 1/2 tablespoon flour, 1 1/2 cup plus 1 1/2 tablespoon white sugar, baking powder, and salt together in a large bowl.
Mix vegetable oil, eggs, and coconut milk together in another bowl. Pour over flour mixture; stir well to combine. Fold shredded coconut and vanilla extract into batter. Spoon batter into prepared muffin tin, filling each liner 2/3 of the way.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 25 minutes. Remove from oven and transfer to a wire rack until cooled completely.
Place chopped chocolate in a bowl.
Heat cream in a small saucepan over medium heat until edges are bubbling, about 5 minutes. Pour over chocolate in the bowl. Mix until ganache is smooth and shiny. Chill until firm, about 1 hour.
Remove ganache from the refrigerator. Beat with an electric mixer on medium speed until fluffy and slightly lightened in color, 3 to 5 minutes. Transfer to a piping bag fitted with a round tip.