Butter a 10 X 15 inch jelly roll pan. Line with parchment paper and butter that as well. Preheat oven to 400° F.
In a mixer (a hand mixer and sturdy deep bowl work as well), beat the eggs until they are very thick and light colored (this takes about 7 minutes). Continue beating and add the sugar in 1 tablespoon at a time, allowing each spoonful to mix in before continuing with the next. Beat in the vanilla as well.
Stop the mixer and sift 1/2 cup sifted cake flour on top of the batter. Using a spatula, gently stir the flour into the batter. Sift the final 1/2 cup flour on top and then very gently fold this into the batter. You want to stop as soon as all the flour is integrated into the batter. This will give you a light and airy cake.
Pour and spread the batter into the prepared pan and bake for just 10 minutes. Do not overbake or the cake will be too stiff to roll without breaking.
As soon as you take it out of the oven, turn the cake out onto a clean dishtowel (I've seen people recommend that you put powdered sugar on the dishtowel so that it doesn't stick, but I don't find this necessary). Remove the parchment paper and allow the cake to cool for a couple of minutes. While it is still warm, roll the cake up from one of its short ends with the dishtowel inside (this way the cake gets used to being rolled and won't tear when you fill it and roll it back up). Allow the cake to cool completely.
Unroll the cake, and spread about 1/2 of the chocolate buttercream (recipe below) evenly on top. Carefully roll the cake back up and neatly place on your serving dish, seam side down.
Optional: To enhance the yule log effect, cut off the ends at an angle and use these to create stubs on the log (they're supposed to look like cut off branches), attaching them with some buttercream.
Frost the outside of the log and, using a fork, trace irregular lines in the frosting to give it a woody effect. Refrigerate the cake for 20 minutes to set the frosting, then cover loosely with plastic wrap and allow it to "age" in the refrigerator for several hours