Preheat the oven to 350 degrees F. Spray two 9-inch cake pans with nonstick spray and line the bottoms with parchment paper.
Sprinkle half of the shredded coconut on a baking sheet. Toast in the oven until golden brown, stirring often, about 15 minutes. Let cool on the baking sheet.
Combine the instant espresso and water in a measuring cup; stir until dissolved. Add to a medium bowl, along with the cake mix, vegetable oil and eggs. Beat for 2 minutes with a handheld mixer on medium speed. Divide the batter between the prepared cake pans and smooth the tops.
Bake until a toothpick inserted in the center of a cake comes out clean, about 25 minutes. Allow the cakes to cool in the pans for 10 minutes, then invert onto a baking rack and let cool completely.
Meanwhile, combine the cream cheese, butter, coconut milk, salt and powdered sugar in a large bowl. Beat with a handheld mixer on medium speed until light, fluffy and smooth, about 4 minutes. Stir in the remaining (untoasted) coconut with a rubber spatula.
If the cakes have domed in the center, trim to level the tops. Place one cake layer, up-side down, on a platter or plate. Spoon one-third of the frosting on top and spread evenly, almost completely to the edge. Place the other layer, up-side down, on top, pressing gently to anchor. Using an offset spatula, evenly frost the entire cake; if the frosting gets too soft, place it in the refrigerator for 15 minutes. Gently press the toasted coconut around the outside of the cake and sprinkle it over the top.