Step 1

Preheat oven to 375°. Coat an 18x13" rimmed baking sheet with nonstick spray. Line with parchment paper and lightly coat parchment. Place a large kitchen towel (it should be larger than baking sheet) on a flat surface. Whisk equal parts cocoa and powdered sugar in a small bowl and dust towel with cocoa mixture with a fine-mesh sieve.

Step 2

Sift flour and ¼ cup cocoa powder into a small bowl. Heat chocolate, oil, and vanilla in a medium microwave-safe bowl in 15-second intervals, stirring occasionally, until melted. Let cool slightly.

Step 3

Using an electric mixer on medium-high speed, beat egg whites and salt in a large bowl until foamy. With motor running, gradually add ⅓ cup granulated sugar and beat until stiff, glossy peaks form.

Step 4

Using clean beaters, beat egg yolks and ⅓ cup granulated sugar in another large bowl until pale and thick, about 4 minutes. Beat in chocolate mixture until no streaks remain, then use a large spatula to fold in meringue, leaving some streaks. Fold in dry ingredients just to combine—be careful not to overmix.

Step 5

Scrape batter into prepared baking sheet; smooth top (you want to have an even layer). Bake until top of cake is dry and springs back when gently pressed and edges are starting to pull away from sides of baking sheet, 10−12 minutes; let cool slightly.

Step 6

Run a knife along the edge of baking sheet to loosen and invert cake onto prepared towel. Peel away parchment and roll cake into a log inside towel. Transfer, seam side down, to a wire rack and let sit until just barely warm, about 20 minutes.

Step 7

Shake remaining 2 Tbsp. granulated sugar and 2 Tbsp. hot water in a jar until sugar is dissolved, about 1 minute. Stir in Cognac. Unroll cake and brush top with syrup.

Step 8

Spread whipped cream over top of cake, leaving a 1" border. Roll up cake and place, seam side down, on a platter. Chill until cold, at least 30 minutes.

Step 9

Dust with powdered sugar and cut into 1" slices just before serving.

Step 10

Instead of whipped cream, spread Chestnut Mousse over top of cake, leaving a 1" border. Roll up cake and place, seam side down, on a platter. Chill until mousse is set, at least 3 hours.

Step 11

Dust with powdered sugar and cut into 1" slices just before serving.

Step 12

Do ahead: Roll can be made 2 days ahead. Cover and keep chilled.

Step 13

Follow instructions for level 2, but do not dust cake with powdered sugar and slice. Instead, using a serrated knife, trim ½" of cake from both ends. Working from one end, gently slice off a 2" piece of cake, cutting at a 45° angle. Cut another 2" piece from same end, this time cutting perpendicular to roll to create a squared off end. Dab 1 Tbsp. buttercream on angled sides of each 2" piece of roll and stick to cake to form branches, positioning 1 on top and 1 on the side. Using and offset spatula or butter knife, spread chocolate buttercream over entire outside of roll, leaving cut ends exposed to reveal spiral). Use spatula to create textured lines in buttercream to look like tree bark.

Step 14

Dust with powdered sugar and decorate with meringue mushrooms just before serving.

Step 15

Do ahead: Buche de Noel (without powdered sugar and mushrooms) can be made 1 day ahead. Cover and chill.