01 - Preheat oven to 350°F. Line a 15×10-inch jelly roll pan with parchment paper and lightly grease the surface.
02 - In a medium bowl, sift together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt until evenly blended.
03 - In a large bowl, beat the eggs and granulated sugar with an electric mixer on high speed for 5 minutes until the mixture becomes thick, pale, and ribbons off the beaters.
04 - Gently fold in the vanilla extract. Gradually add the sifted dry ingredients, alternating with the milk, folding until just combined. Do not overmix.
05 - Spread the batter evenly across the prepared jelly roll pan. Bake for 10 to 12 minutes, or until the cake springs back when lightly pressed.
06 - While the cake bakes, lay a clean kitchen towel flat and dust it generously with powdered sugar. Immediately upon removing the cake from the oven, invert it onto the towel. Carefully peel off the parchment paper.
07 - Starting at the short end, tightly roll the cake and towel together. Place seam-side down on a wire rack and allow to cool completely, about 45 minutes.
08 - Gently unroll the cooled cake. Spread the creamy caramel sauce evenly over the entire surface. Sprinkle the toasted chopped pecans in an even layer over the caramel.
09 - Carefully roll the cake back up, this time without the towel. Place it seam-side down on a serving platter.
10 - Heat the heavy cream and unsalted butter in a small saucepan until just simmering. Pour the hot mixture over the chopped semi-sweet chocolate in a heatproof bowl. Let sit for 2 minutes, then whisk until completely smooth. Allow to cool slightly until it thickens to a pourable consistency.
11 - Pour the ganache over the rolled cake, spreading it evenly across the top and sides. Garnish with additional chopped pecans, a caramel drizzle, and chocolate shavings as desired.
12 - Refrigerate for at least 30 minutes before slicing to ensure clean, neat portions. Allow to come to room temperature before serving for the best texture and flavor.