Preheat oven to 350 degrees F. Coat a 9 x 13-inch pan with non-stick cooking spray and set aside.
Add all ingredients except coconut milk to a large bowl or stand mixer fitted with a whisk attachment. Pour the batter into the prepared baking pan and bake for 30 to 35 minutes until toothpick comes clean from the center of the cake.
Poke holes in the warm cake and pour the coconut milk over the cake, make sure to shake and stir the coconut milk first. Use a spoon to spread the coconut milk around to help it get in all the holes. Let soak for 2 hours.
Frosting
Add heavy cream, confectioners' sugar, and pudding mix to a large bowl or stand mixer fitted with a whisk attachment and whip on medium-high speed until light and fluffy. Spread the frosting over the cake and sprinkle with shredded coconut.