01 - Preheat oven to 350°F. Line a 10x15-inch jelly roll pan with parchment paper and lightly grease the surface.
02 - In a large mixing bowl, beat the eggs with granulated sugar and vanilla extract using an electric mixer for 5 minutes, until the mixture turns pale, thick, and forms ribbons when lifted.
03 - Sift together the all-purpose flour, cocoa powder, baking powder, and salt. Gently fold the sifted mixture into the beaten eggs until just combined, taking care not to deflate the batter.
04 - Pour the batter into the prepared jelly roll pan and spread it into an even layer. Bake for 10 to 12 minutes, or until the cake springs back lightly when pressed with a fingertip.
05 - While the cake is still hot, invert it onto a clean kitchen towel dusted with powdered sugar. Peel away the parchment paper. Starting from one short end, roll the cake up inside the towel into a tight log. Allow it to cool completely in this shape.
06 - Once the cake has cooled completely, carefully unroll it. Spread the caramel sauce evenly across the surface, reserving about 2 tablespoons for drizzling later. Scatter the chopped toasted pecans in an even layer over the caramel.
07 - Gently but firmly roll the cake back up, this time without the towel. Place the roll seam-side down on a serving platter.
08 - Place the chopped semi-sweet chocolate in a heatproof bowl. Heat the heavy cream until just simmering, then pour it over the chocolate. Let it sit for 2 minutes, then stir until the ganache is glossy, smooth, and slightly thickened.
09 - Pour the ganache over the cake roll, allowing it to flow down the sides naturally. Drizzle with the reserved caramel sauce and arrange pecan halves on top as garnish.
10 - Refrigerate the cake roll for 20 minutes to set the ganache before slicing. For the best texture and flavor, bring to room temperature before serving.