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 approximately 5 minutes, until the mixture turns pale yellow and falls in thick ribbons from the beaters.
03 - Sift together the all-purpose flour, cocoa powder, baking powder, and salt. Gently fold the sifted dry ingredients into the egg mixture using a spatula, mixing only until just combined to avoid deflating the batter.
04 - Pour the batter into the prepared jelly roll pan and spread it into an even, thin layer. Bake for 10 to 12 minutes, until the sponge springs back lightly when gently pressed with a fingertip.
05 - While the sponge is still hot, invert it onto a clean kitchen towel that has been dusted with powdered sugar. Carefully peel away the parchment paper. Starting from one short end, roll the cake up snugly inside the towel. Allow it to cool completely in this rolled shape.
06 - Once fully cooled, gently unroll the sponge. Spread the caramel sauce evenly across the entire surface, reserving about 2 tablespoons for finishing. Scatter the chopped toasted pecans in an even layer over the caramel.
07 - Carefully roll the cake back up, this time without the towel, keeping it rolled snugly. 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 it just begins to simmer, then pour it over the chocolate. Let it sit undisturbed for 2 minutes, then stir gently until the ganache is glossy, smooth, and slightly thickened.
09 - Pour the ganache over the top of the cake roll, allowing it to flow naturally down the sides. Drizzle with the reserved caramel sauce and arrange pecan halves along the top as a garnish.
10 - Refrigerate the cake roll for at least 20 minutes before slicing to allow the ganache to set and the layers to firm up. For the best texture and flavor, bring to room temperature before serving.