Yule Log

1. Preheat to 400 degrees and position rack in the middle.
2. Fill a medium saucepan halfway with water and bring it to a boil.
3. Whisk the eggs, egg yolks, salt, and sugar together in the bowl of an electric mixer. Place over the pan of simmering water and whisk gently until the mixtureis just lukewarm, about 100 degrees if you have a thermometer (or test with your finger—it should be warm to the touch).
4. Remove bowl from heat and whip on medium- high speed with an electric mixer fitted with the whisk attachment until the egg mixture is cooled (touch the outside of the bowl to tell) and tripled in volume. The egg foam will be thick and will form a slowly dissolving ribbon falling back onto the bowl of whipped eggs when the whisk is lifted.
5. While the eggs are whipping, stir together the flour and cornstarch.
6. Sift one-third of the flour mixture over the beaten eggs. Use a rubber spatula to fold in the flour mixture, making sure to scrape all the way to the bottom of the bowl on every pass through the batter to prevent the flour mixture from accumulating there and making lumps. Repeat twice.
7. Scrape the batter into the prepared pan and smooth the top. Bake the genoise for about 10 to 12 minutes. Make sure the cake doesn’t overbake and become too dry or it will not roll properly.
8. Once the cake is done (a tester will come out clean and if you press the cake lightly it will spring back), remove it from the oven and let it cool on a rack.

Chocolate Buttercream

1. Pour the water and sugar into a 1-quart heavy-bottomed saucepan and place over medium-high heat. When the bubbles start to form around the edge of the pan, insert a candy thermometer in the mixture.
2. Place the egg whites in a large mixing bowl and whip with an electric mixer on medium-high speed until foamy and slightly holding soft peaks. The sugar is ready when it reaches 250 degrees, what is known as the soft-ball stage.
3. Pour the cooked sugar down the side of the bowl while continuing to whip the egg whites.
4. Continue whipping the meringue on medium-high speed until the outside of the bowl is warm but not hot, about 5 minutes. Add the butter all at once and beat on medium speed until incorporated. Increase the mixer speed to medium-high and whip until the buttercream is thick, smooth, and shiny, about 10 minutes. At this stage, slowly pour in the chocolate and beat for another 30 seconds or so.
5. The buttercream can be used immediately or can be stored in the refrigerator for 3 to 4 days or in the freezer for several weeks if kept in an airtight container. If it has been chilled or frozen, allow the buttercream to come to room temperature before using, then whip it with an electric mixer on medium speed until it returns to its initial volume and is once again thick, smooth, and shiny.