For the cake: Preheat the oven to 350 degrees F. Grease an 8-inch round cake pan with cooking spray and line the bottom with parchment paper.
Whisk together the granulated sugar, all-purpose flour, cake flour, baking powder, baking soda and salt in a large bowl. Whisk together the egg, coconut milk, lemon juice, vanilla and coconut extract in a medium bowl until combined. Whisk in the coconut oil. Add the wet ingredients to the dry ingredients and stir to combine. Pour the batter into the cake pan.
Bake until a toothpick inserted in the center comes out clean, 25 to 30 minutes.
Let cool in the pan for 10 minutes, then remove to a rack to cool completely.
For the frosting: Beat the butter with a stand mixer fitted with the paddle attachment on medium speed until creamy. Reduce the speed to low and gradually add the powdered sugar, beating to combine. Beat in the salt, vanilla and coconut milk.
For the assembly: To make the cake balls, crumble the cake into a large bowl with your hands. Mix in the coconut, then mix in the frosting until it's combined. Line a quarter-sheet pan with parchment paper. Roll smooth 1/4-cup-sized balls and place on the parchment. Freeze until firm to the touch, about an hour.
Melt the white chocolate in a double boiler or a microwave for 30-second increments, stirring after each. Stir in the oil. Add a few drops of food coloring, if using, and swirl it around. Do not mix it all the way together, so that the swirl is still visible. Using two forks, dip the chilled balls in the chocolate to coat evenly, then allow any excess to drip off. Place back on the parchment to harden at room temperature, about 30 minutes. Before it fully hardens, add three chocolate chips to each to look like a bowling ball!