Preheat your oven to 375°F. Grease a 10x15 inch baking sheet, line it with parchment paper, and grease the parchment paper too. Set aside. Lay a clean, lint-free kitchen towel flat on the counter and dust it generously with ¼ cup unsweetened cocoa powder — this prevents the cake from sticking when you roll it.

In a mixing bowl, whisk together the sifted ½ cup all-purpose flour, ¼ cup unsweetened cocoa powder, 1 tsp baking powder, and ¼ tsp fine salt. Set aside.

Separate the 4 eggs into two large mixing bowl. Beat the 4 eggs yolks with ½ cup of the sugar and the 1 tsp vanilla extract on high speed until the mixture is thick, pale yellow, and falls in ribbons from the beater — about 3–4 minutes. Set aside.

In a clean mixing bowl with clean beaters, beat the 4 eggs whites on medium speed until foamy. Gradually add the remaining ¼ cup of sugar and beat on high until stiff, glossy peaks form — about 3–4 minutes. Do not overbeat.

Gently fold the dry ingredients into the 4 eggs yolk mixture using a spatula until just combined. Then fold in one-third of the whipped 4 eggs whites to lighten the batter, followed by the remaining whites in two additions. Fold gently — do not deflate the whites. The batter will be light and airy.

Spread the batter evenly into the prepared baking sheet using an spatula, reaching all four corners. Bake for 10–12 minutes, until the cake springs back when lightly touched in the center and a toothpick comes out clean. Do not overbake — a dry sponge will crack when rolled.

Immediately upon removing from the oven, run a knife around the edges. Flip the hot cake directly onto the ¼ cup unsweetened cocoa powder-dusted kitchen towel. Carefully peel off the parchment paper. Starting from a short end, roll the cake up tightly inside the kitchen towel. Place seam-side down on a wire rack and let cool completely — about 1 hour. Rolling it while warm is the key to preventing cracks later.

While the cake cools, make the filling. In a cold mixing bowl, beat the cold 1 ½ cups heavy cream, 3 tbsp confectioners' sugar, and 1 tsp vanilla extract on medium-high speed until stiff peaks form — about 3 minutes. Do not overwhip. Refrigerate until ready to use.

Beat the softened unsalted butter on medium speed until smooth and fluffy, about 2 minutes. Add the sifted ¼ cup unsweetened cocoa powder, 3 tbsp confectioners' sugar, 1 tsp vanilla extract, and ¼ tsp fine salt. Mix on low to combine, then increase to medium-high. Add 1 ½ cups heavy cream one tablespoon at a time until the buttercream is smooth, spreadable, and holds its shape. It should be thick but not stiff. Set aside at room temperature.

Once the cake is completely cool, carefully unroll it from the kitchen towel — it's okay if it curls slightly, that's normal. Spread the whipped 1 ½ cups heavy cream filling evenly across the surface, leaving a ½-inch border on all edges to prevent overflow when rolling.

Re-roll the cake tightly (without the kitchen towel this time), using the kitchen towel to guide and support it. Place seam-side down on a serving platter or baking sheet lined with parchment paper.

Using a sharp serrated knife, cut a 2-inch diagonal slice off one end of the log. Place this cut piece against the side of the log to create a 'branch' knot — this is the signature Yule log look. Secure it with a little buttercream if needed.

Spread the chocolate buttercream all over the log and the branch piece using an spatula, covering the entire surface including the ends. Once covered, drag a knife lengthwise along the buttercream in long, wavy strokes to create a realistic bark texture. Swirl the knife in a circle on the cut ends to mimic tree rings.

Refrigerate the assembled log for at least 30 minutes to set the buttercream and allow the flavors to meld. Just before serving, dust lightly with 3 tbsp confectioners' sugar to mimic snow, and garnish with 1 bunch of rosemary and 6 pieces of cranberries if desired.