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 mixer for 5 minutes, until the mixture turns pale, thick, and falls in ribbons.
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, taking care not to deflate the batter.
04 - Pour the batter into the prepared pan and spread it into an even layer. Bake for 10 to 12 minutes, until the sponge springs back lightly when touched in the center.
05 - While still hot, invert the sponge onto a clean kitchen towel dusted with powdered sugar. Peel away the parchment paper. Starting from one short end, roll the sponge and towel together into a log shape. Allow to cool completely while rolled.
06 - Once cooled, carefully unroll the sponge. Spread the caramel sauce evenly over the entire surface, reserving about 2 tablespoons for finishing. Scatter the chopped toasted pecans in an even layer over the caramel.
07 - Gently re-roll the sponge, this time without the towel, keeping it snug but not overly 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 simmering, then pour it over the chocolate. Let stand 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 cascade down the sides. Drizzle with the reserved caramel sauce and arrange pecan halves on top as garnish.
10 - Refrigerate the roll for 20 minutes to set the ganache before slicing. For the best texture and flavor, allow slices to come to room temperature before serving.