01 - Preheat oven to 350°F (175°C). 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. Set aside.
03 - In a large mixing bowl, beat the eggs and granulated sugar with an electric mixer on high speed for 5 minutes until the mixture is thick, pale, and forms ribbons when lifted.
04 - Gently fold in the vanilla extract. Gradually add the sifted dry ingredients, alternating with the milk, folding carefully until just combined. Do not overmix.
05 - Spread the batter evenly into the prepared jelly roll pan. Bake for 10 to 12 minutes, or until the top springs back lightly when touched.
06 - While the cake bakes, lay a clean kitchen towel flat on the counter and dust generously with powdered sugar. As soon as the cake comes out of the oven, invert it onto the towel. Carefully peel off the parchment paper. Starting at a short end, tightly roll the cake and towel together. Place seam-side down on 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. Place it 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 smooth and glossy. Allow to cool slightly until it thickens to a pourable consistency.
10 - Pour the ganache over the rolled cake, spreading evenly across the top and allowing it to drip down the sides. Garnish with additional chopped pecans, a drizzle of caramel, and chocolate shavings. Refrigerate for at least 30 minutes before slicing for clean, neat portions. Serve at room temperature.