01 - Preheat oven to 350°F. Line a 10x15-inch jelly roll pan with parchment paper and lightly grease the surface.
02 - In a mixing bowl, beat the eggs with granulated sugar and vanilla extract using an electric or stand mixer for 5 minutes, until the mixture turns pale and thick.
03 - Sift together the all-purpose flour, cocoa powder, baking powder, and salt. Gently fold the dry mixture into the beaten egg mixture until just combined, being careful 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, until the cake springs back lightly when touched.
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 the short end, roll the cake up inside the towel into a log shape. Allow it to cool completely while rolled.
06 - Once the sponge has cooled completely, carefully unroll it. Spread the caramel sauce evenly across the surface, reserving about 2 tablespoons for drizzling later. Sprinkle the chopped toasted pecans in an even layer over the caramel.
07 - Gently re-roll the cake tightly without the towel. Place it seam-side down on a serving platter.
08 - Place the chopped semi-sweet chocolate in a heatproof bowl. Heat the heavy cream until hot but not boiling, then pour it over the chocolate. Let it sit for 2 minutes, then stir until the mixture becomes glossy and smooth. Allow the ganache to thicken slightly before using.
09 - Pour the ganache over the assembled cake roll, letting it drip down the sides naturally. Drizzle with the reserved caramel sauce and arrange pecan halves on top as a garnish.
10 - Refrigerate the cake roll for 20 minutes before slicing to achieve clean, neat portions. Allow it to come to room temperature before serving for the best texture and flavor.