Preheat your oven to 375°F and prepare a sheet pan (approximately 9x13 inches or similar size) by lining it with parchment paper and lightly spraying with cooking spray. While the oven heats, bring your 4 eggs to room temperature—this is crucial because room temperature eggs whip to greater volume, creating a lighter, airier cake. Beat the eggs alone for 3 minutes until they become pale and frothy. Gradually add the 1 1/8 cup sugar while continuing to beat for another 6-10 minutes until the mixture reaches the ribbon stage (thick, pale, and falls in ribbons when you lift the beater). This long beating time incorporates air, which is your primary leavening agent in this delicate sponge cake.
Gently stir the 2 tbsp milk and 1 tsp coconut essence into the egg mixture. In a separate small bowl, whisk together the 1 1/4 cups flour, 1 tsp baking powder, and 1/4 tsp salt. Fold this dry mixture into the wet ingredients using a spatula, being careful not to deflate the eggs—fold just until no streaks of flour remain. Pour the batter onto your prepared pan and spread it into an even layer. Bake for 13-16 minutes until a toothpick inserted in the center comes out clean and the cake is lightly golden. The cake should spring back when lightly touched.
While the cake bakes, lay out a clean kitchen towel and dust it evenly with the 1/4 cup powdered sugar—this prevents sticking and adds subtle sweetness to the exterior. When the cake comes out of the oven, immediately turn it out onto the prepared towel. Carefully peel away the parchment paper. Working quickly while the cake is still warm (warmth makes it pliable), roll the cake tightly in the towel and set it aside to cool completely, about 30 minutes. I like to let it cool seam-side down so it holds its shape better; the towel acts as a mold that helps prevent cracking.
While the cake cools, prepare the frosting. Using an electric mixer, beat the 18 oz softened cream cheese, 1 1/4 cup sugar, 1/8 tsp salt, and 1 tsp coconut essence together until smooth and creamy, about 2-3 minutes. Make sure to scrape down the bowl as you go. In a separate bowl, whip the 1.75 cups chilled heavy cream with the 1/2 tsp vanilla extract and 1/2 cup sifted powdered sugar until stiff peaks form. I prefer chilled cream because it whips faster and holds its structure better, especially important in a frosting that will sit in the fridge. Gently fold the whipped cream into the cream cheese mixture just until combined, being careful not to deflate the peaks.
Once the cake has cooled completely, carefully unroll it from the towel. Spread about one-third of the frosting from Step 4 evenly over the cake, leaving a small border around the edges. Sprinkle 1 cup of the sweetened shredded coconut over the frosting. Tightly roll the cake back up (without the towel this time), using the bare edge to seal it. Place the roll seam-side down on a serving plate or cake board. Spread the remaining frosting over the outside of the roll, creating an even coating. Press the remaining 1.5 cups coconut all over the outside, covering it completely for that signature look.
Refrigerate the finished cake roll for 1-2 hours before serving. This chilling time allows the frosting to set and makes slicing much cleaner. The roll will hold together better when cold, and the flavors will have time to meld beautifully. Slice with a sharp, warm knife, wiping it between cuts for neat presentation.