01 - Preheat oven to 350°F. Line a 10×15-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 is pale and thick.
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 pan and spread evenly. Bake for 10 to 12 minutes, until the cake springs back lightly when touched.
05 - While still hot, invert the cake onto a clean kitchen towel dusted with powdered sugar. Peel off the parchment paper. Starting at the short end, roll the cake and towel together into a log. Let cool completely in this shape.
06 - Once completely cool, gently unroll the cake. Spread the caramel sauce evenly over the surface, reserving about 2 tablespoons for drizzling. Sprinkle the chopped toasted pecans evenly over the caramel layer.
07 - Carefully re-roll the cake without the towel, keeping it snug but gentle. Place 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 sit for 2 minutes, then stir until the ganache is glossy and smooth. Allow it to thicken slightly.
09 - Pour the ganache over the cake roll, letting it drip naturally down the sides. Drizzle with the reserved caramel sauce and garnish with pecan halves.
10 - Refrigerate for 20 minutes before slicing to set the filling and glaze. For the best texture and flavor, serve at room temperature.