Step 1: Preheat and Prepare

Preheat your oven to 350°F (175°C). Proper oven temperature is crucial for even baking, ensuring the cake bakes through without drying out. Line a 15×10-inch jelly roll pan with parchment paper. This step is essential as it allows for easy removal of the cake after baking, preventing it from sticking and tearing. Extend the parchment paper slightly over the edges of the pan to create handles for lifting the cake out.

Step 2: Prepare the Batter

In a large bowl, beat the egg yolks with half of the granulated sugar until the mixture becomes thick and pale. This process, known as creaming, incorporates air into the yolks, which is vital for creating a light and airy cake. The pale color indicates that enough air has been incorporated.

Add the milk and vanilla extract to the egg yolk mixture, blending until smooth. Milk adds moisture to the cake, while vanilla extract enhances the overall flavor profile.

In a separate bowl, sift together the all-purpose flour, cocoa powder, baking powder, and salt. Sifting ensures that the dry ingredients are evenly distributed and free of lumps, which is critical for a uniform cake texture. Cocoa powder adds the characteristic chocolate flavor and color, baking powder acts as a leavening agent to help the cake rise, and salt enhances the other flavors.

Step 3: Incorporate Ingredients

Gradually fold the dry ingredients into the egg yolk mixture, blending carefully to retain air. It's important to fold the dry ingredients gently to avoid overmixing, which can develop gluten and result in a tough cake. Incorporate the dry ingredients in small batches, mixing until just combined after each addition.

Step 4: Beat Egg Whites

In a separate, clean bowl, whisk the egg whites until soft peaks form. Use an electric mixer for best results. Ensure that the bowl and beaters are clean and free of grease, as any residue can prevent the egg whites from whipping properly. Soft peaks are formed when the egg whites hold their shape but the tips droop slightly.

Gradually add the remaining granulated sugar to the egg whites, beating until stiff peaks form. Stiff peaks are formed when the egg whites stand up straight and hold their shape firmly. Be careful not to overwhip, as this can cause the egg whites to become dry and grainy.

Step 5: Combine and Bake

Gently fold the egg whites into the chocolate batter in three batches. This technique helps to maintain the airiness of the egg whites, resulting in a light and fluffy cake. Fold gently, using a spatula, and avoid stirring or mixing vigorously.

Pour the batter evenly into the prepared pan and spread it out to the edges with a spatula. A uniform layer of batter ensures even baking.

Bake for 10-12 minutes, or until a toothpick inserted into the center comes out clean. The baking time may vary depending on your oven, so check the cake frequently to prevent overbaking. A clean toothpick indicates that the cake is fully baked.

Step 6: Rolling the Cake

While the cake is still warm, carefully invert it onto a clean kitchen towel dusted with powdered sugar. The powdered sugar prevents the cake from sticking to the towel. Gently peel off the parchment paper.

Starting from one of the short ends, roll the cake up tightly in the towel. Rolling the cake while it's still warm helps to prevent it from cracking. Allow the rolled cake to cool completely in the towel. This allows the cake to set in the rolled shape.

Step 7: Prepare the Filling and Assemble

While the cake is cooling, prepare the chocolate ganache. Place the finely chopped semi-sweet chocolate in a heatproof bowl. In a saucepan, heat the heavy cream until it just comes to a simmer. Pour the hot cream over the chocolate and let it sit for a minute to allow the chocolate to melt.

Gently whisk the chocolate and cream together until smooth and glossy. If the ganache is too thick, add a tablespoon of hot cream at a time until it reaches the desired consistency.

Once the cake has cooled completely, carefully unroll it. Spread the sweetened condensed milk evenly over the surface of the cake. Sweetened condensed milk adds a creamy, sweet layer to the filling.

Sprinkle the toasted coconut and chopped pecans evenly over the condensed milk. Toasting the coconut and pecans enhances their flavor and adds a pleasant crunch to the filling.

Carefully roll the cake back up tightly. Use the towel to help you guide the cake as you roll it.

Step 8: Decorate with Ganache

Place the rolled cake on a serving platter. Drizzle the prepared chocolate ganache over the top of the cake. The ganache adds a rich, decadent chocolate layer to the cake.

Sprinkle additional toasted coconut and chopped pecans over the ganache for garnish. This adds visual appeal and reinforces the flavors of the filling.

Refrigerate the cake for at least 30 minutes to allow the ganache to set before slicing and serving. This helps to prevent the ganache from being too messy when cutting.