Preheat the oven to 350°F Lightly spritz three 9-inch round cake pans with cooking spray and line the bottoms with parchment paper.

To make the cakes: In a medium bowl, whisk together the flour, cocoa powder, baking soda, baking powder, and salt.

In a large bowl, whisk together the buttermilk, coffee, brown sugar, oil, granulated sugar, eggs, egg yolk, and vanilla until smooth.

In three additions, sift the flour mixture into the wet mixture, whisking vigorously after each addition until the batter is smooth and glossy. Divide the batter evenly among the prepared cake pans, about 510 grams (a little less than 2 cups) per pan.

Bake until fragrant and the center springs back when touched, 20 to 25 minutes. Let the cakes cool completely in the pans.

To make the cocoa cream cheese frosting: In the bowl of a stand mixer fitted with the whisk attachment (or in a large bowl with a whisk or handheld mixer), whisk the cream on medium-high speed until stiff peaks form, about 4 minutes. Transfer the whipped cream to a small bowl and place it in the refrigerator.

In the same bowl of the stand mixer (no need to clean) fitted with the whisk attachment, whisk the cream cheese on medium speed until smooth and fluffy, 1 to 2 minutes.

Add the powdered sugar and whisk until smooth. Scrape down the sides and bottom of the bowl with a rubber spatula.

Add the cocoa powder, vanilla, and salt and whisk on low speed until incorporated, stopping to scrape down the sides and bottom of the bowl as needed.

Using a rubber spatula, little by little, fold in the whipped cream until incorporated. Taste and season with more salt, if desired. Transfer one-quarter of the frosting to a piping bag. Refrigerate all the frosting for 30 minutes.

Line a deep 9-inch round cake pan or pot with plastic, ensuring plenty of overhang.

Invert one cake round into the bottom of the prepared cake pan, bottom-side up. Dollop about ⅓ cup of frosting onto the cake and spread it evenly with an offset spatula. Pipe a dam of frosting around the perimeter of the cake to ensure the custard doesn’t ooze out of the cake.

Using an offset spatula, cover the cake evenly with about ¾ cup of the salty coconut custard.

Invert the second cake onto the custard and repeat with the layer of frosting, the frosting dam, and the coconut custard.

Finally, place the third cake on top, bottom-side up.

Wrap the pot tightly in plastic and refrigerate for at least 1 hour or up to 24 hours. Store any unused frosting in an airtight container and refrigerate for up to 4 days. (The cake can also be stored in the freezer, wrapped in plastic, for up to 3 months; thaw the cake in the refrigerator for 24 hours.) Allow the frosting to come to room temperature before use, about 2 hours.

Invert the cake onto a cardboard cake round or serving platter. Remove the cake pan, then peel off the plastic.

Spread a thin layer of frosting all over the top and sides of the cake. (This is a crumb coating—you will add more frosting in the next step.) Smooth with an offset spatula and return to the refrigerator for 15 minutes.

Spread a thick layer of frosting all over the top and sides of the cake. To perfectly smooth the frosting, fill a bowl with hot water and dip the offset spatula into it. Holding the spatula flush to the cake, turn the cake until the coating is smooth.

Sprinkle the coconut flakes all over the sides and top of the cake. Serve immediately.