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, fluffy, and falls in thick ribbons from the beaters.
03 - Sift together the all-purpose flour, cocoa powder, baking powder, and salt. Gently fold the dry mixture into the whipped egg base 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, until the top springs back lightly when pressed with a fingertip.
05 - While the cake is still warm, invert it onto a clean kitchen towel that has been dusted with powdered sugar. Peel away the parchment paper. Starting from one short end, roll the cake up snugly inside the towel. Let it cool completely in this shape to set the spiral.
06 - Once fully cooled, carefully unroll the sponge. Spread the caramel sauce evenly across the surface, reserving about 2 tablespoons for finishing. 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 it 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 undisturbed for 2 minutes, then stir from the center outward until the ganache is glossy, smooth, and slightly thickened.
09 - Pour the ganache over the cake roll, allowing it to flow naturally down the sides. Drizzle the reserved caramel sauce over the top and arrange pecan halves as a finishing garnish.
10 - Refrigerate the roll for at least 20 minutes to set the ganache before slicing. Allow it to come to room temperature for the best texture before serving.