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 uniformly blended.
03 - In a large mixing bowl, beat the room-temperature eggs and granulated sugar with an electric mixer on high speed for 5 minutes until the mixture is thick, pale, and forms ribbons when the beaters are lifted.
04 - Gently fold the vanilla extract into the egg mixture. Gradually incorporate the sifted dry ingredients, alternating with the milk, folding carefully until just combined and no dry streaks remain.
05 - Spread the batter evenly across the prepared jelly roll pan. Bake for 10 to 12 minutes, or until the top springs back lightly when touched and a toothpick inserted in the center comes out clean.
06 - While the cake bakes, lay a clean kitchen towel flat on the counter and dust generously with powdered sugar. Immediately upon removing the cake from the oven, invert it onto the prepared towel. Peel away the parchment paper. Starting from a short end, tightly roll the cake and towel together. Transfer to a wire rack and cool completely, about 45 minutes.
07 - Gently unroll the cooled cake. Spread the creamy caramel sauce evenly over the entire surface. Sprinkle the toasted chopped pecans uniformly over the caramel layer.
08 - 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.
09 - In a small saucepan, heat the heavy cream and unsalted butter over medium heat 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 and glossy. Allow to cool slightly so it thickens to a pourable consistency.
10 - Pour the slightly cooled ganache over the rolled cake, spreading evenly with a spatula to coat the top and sides. Garnish with additional chopped pecans, a drizzle of caramel, and chocolate shavings as desired.
11 - Refrigerate the assembled cake roll for at least 30 minutes to allow the ganache to set and the filling to firm up for clean slicing. Wipe the knife blade between cuts for neater portions. Serve at room temperature for the best flavor and texture.