Preheat the oven to 350°F.
Prepare the cake mix according to the package instructions, using the eggs, water, and oil listed on the box. Stir in the coconut extract until combined.
1 (15.25 oz./432 g) box white cake mix, 1 tsp. (4 g) coconut extract
Pour the batter into a 9x13-inch baking dish and bake according to the box directions, or until a toothpick inserted in the center comes out clean.
While the cake bakes, spread the shredded coconut on a baking sheet. Toast in the oven for 2 to 4 minutes, stirring once or twice, until golden brown. Watch closely—it browns fast. Remove from the oven and transfer to a bowl to cool.
1½ cups (120 g) sweetened shredded coconut
Let the cake cool for about 15–20 minutes, then use the handle of a wooden spoon to poke holes all over the surface.
In a bowl, whisk together the sweetened condensed milk and cream of coconut until smooth. Pour the mixture evenly over the cake, spreading it gently to help it fill the holes.
¾ cup (177 ml) sweetened condensed milk, ½ cup (120 ml) cream of coconut
Once the cake has cooled completely, spread the whipped topping over the surface.
8 oz. (227 g) whipped topping
Sprinkle 1 to 1 1/2 cups of the toasted coconut evenly over the top.
Cover and refrigerate the cake for at least 4 hours before serving, or overnight for best texture.