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Preheat oven to 350 F and place the oven rack in the center of the oven. Line a 17 x 12 inch (43 x 30 cm) baking pan with buttered and floured parchment paper.
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While the eggs are still cold, separate the eggs, placing the whites in one bowl and the yolks in another. Cover and bring to room temperature before using (about 30 minutes).
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Meanwhile melt the chocolate in a heatproof bowl placed over a saucepan of simmering water. Remove from heat and cool.
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Using a hand mixer, add ¼ cup of sugar into the bowl with egg yolks. Beat until light and fluffy (about five minutes - when you slowly raise the beaters, the batter will fall back into the bowl in a slow ribbon.) Beat in the vanilla extract. Scrape down sides of bowl. Add the melted chocolate and beat only to combine.
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Using a hand mixer, beat the egg whites until foamy. Add the cream of tartar and beat at medium-high speed until soft peaks form. Gradually beat in the remaining 2 tablespoons sugar until stiff peaks form.
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Gently fold a small amount of the egg whites into the egg yolk mixture using a rubber spatula. Fold in the remaining whites just until incorporated. Don't over mix or the batter will deflate. Spread the batter evenly into the prepared pan. Bake until the cake is puffed, has lost its shine, and springs back when gently pressed, about 15 - 17 minutes. Remove from the oven.
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Place a second sheet of parchment paper on top of the cake and gently roll lengthwise into a log. Let the cake cool on the counter.
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In a small bowl, mix together Amaretto and Baileys. Unroll the cake and remove the top parchment paper (keep the bottom parchment on). Evenly brush the mixture over the cake and let it soak in while you make the chocolate whip cream.