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 is pale, thick, and ribbon-like.
03 - Sift together the all-purpose 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 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 cake is still hot, invert it onto a clean kitchen towel dusted with powdered sugar. Peel off the parchment paper. Starting from the short end, roll the cake up inside the towel into a log shape. Allow it to cool completely while rolled.
06 - Once the cake is completely cool, gently unroll it. Spread the caramel sauce evenly across the surface, reserving about 2 tablespoons for drizzling later. Sprinkle 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 snug but gentle to avoid cracking. 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 just simmering, 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 naturally down the sides. Drizzle the reserved caramel sauce over the top and arrange pecan halves as a garnish.
10 - Refrigerate the cake roll for 20 minutes to allow the ganache to set before slicing. For the best texture and flavor, serve at room temperature.