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 for 5 minutes, or until the mixture turns pale and thick.
03 - Sift together the 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 pan and spread it into an even layer. Bake for 10 to 12 minutes, until the cake springs back when lightly touched.
05 - While still hot, invert the cake 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 in this rolled position.
06 - Once cooled, carefully unroll the cake. Spread the caramel sauce evenly over the surface, reserving about 2 tablespoons for drizzling later. Sprinkle the chopped toasted pecans in an even layer over the caramel.
07 - Gently roll the cake back up, this time without the towel. Place it seam-side down on a serving platter.
08 - In a heatproof bowl, pour hot heavy cream over the chopped semi-sweet chocolate. Let it sit for 2 minutes, then stir until smooth and glossy. Allow the ganache to thicken slightly before using.
09 - Pour the ganache over the cake roll, letting it drip naturally down the sides. Drizzle with the reserved caramel sauce and arrange pecan halves on top as garnish.
10 - Refrigerate for 20 minutes to set the ganache before slicing. For the best texture and flavor, serve at room temperature.