Preheat your oven to 350°F (175°C) and line a 15x10 inch jelly roll pan with parchment paper, then lightly grease it.
In a large bowl, beat the eggs and granulated sugar with an electric mixer on high speed until thick and pale, about 5-7 minutes. Add the vanilla extract and mix until combined.
In another bowl, sift together the flour, cocoa powder, baking powder, and salt. Gradually fold the dry ingredients into the egg mixture until just combined.
Carefully fold in the melted butter until the batter is smooth, ensuring not to over mix.
Pour the batter into the prepared pan and spread it evenly. Bake for 12-15 minutes, until the surface springs back when touched.
While the cake is baking, prepare a clean kitchen towel by dusting it with powdered sugar. Once the cake is done, immediately invert it onto the towel, peel off the parchment paper, and roll the cake up tightly in the towel from the short end. Allow it to cool completely while rolled up.
For the filling, heat the heavy cream in a saucepan over medium heat until it simmers. Remove it from the heat and add the chopped dark chocolate, stirring until smooth. Let it cool slightly before whisking it to soft peaks.
Unroll the cooled cake gently and spread a layer of the chocolate ganache evenly over the surface, followed by a drizzle of caramel sauce and a sprinkle of crushed praline pecans.
Roll the cake back up, this time without the towel, and place seam-side down on a serving platter.
For the frosting, reheat the remaining chocolate ganache until it is pourable. Pour it over the Yule log, allowing it to drip down the sides.
Decorate with more crushed praline pecans and dust with powdered sugar for a snowy effect.
Notes
Serve on a wooden board or festive platter, garnished with fresh mint leaves or additional praline pecans for an elegant touch.