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, thick, and forms ribbons when lifted.
03 - Sift together the all-purpose flour, cocoa powder, baking powder, and salt. Gently fold the dry mixture into the whipped 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, or until the cake springs back lightly when touched in the center.
05 - While the sponge 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 and towel together into a 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 later drizzling. Sprinkle the chopped toasted pecans over the caramel layer.
07 - Gently roll the cake back up without the towel, keeping it snug but not too tight. 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 hot but not boiling, 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, allow it to come to room temperature before serving.