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1
Place the chocolate in a medium bowl and set aside.
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2
Combine the milk and all but 1 tablespoon of the sugar in a small saucepan.
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3
Heat over medium heat, stirring constantly until the sugar is completely dissolved.
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4
Stop stirring and cook until the milk begins to bubble around the edge of the pan.
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5
Remove the pan from the heat.
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6
Whisk together the egg yolk and the remaining 1 tablespoon sugar in a small bowl.
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7
Pour half of the hot milk over the yolk mixture, whisking constantly, until the mixture thickens slightly and reaches 183 degrees on an instant-read thermometer.
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8
Immediately pour the mixture over the chocolate.
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9
Whisk until the chocolate is melted.
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10
Add the butter 1/2 tablespoon at a time, whisking until the butter is melted and the mixture is smooth.
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11
Whisk in the vanilla.
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12
Scrape the batter into a 6-inch round cake pan and smooth the top with a rubber spatula.
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13
Cover the pan with a plastic wrap and place it in the freezer for at leas 6 hours, or overnight.
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14
To unmold the cake, carefully immerse the pan in hot water for a few seconds.
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15
Wipe the bottom and side of the pan dry and invert the cake onto a serving platter.
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16
Decorate the top of the cake by running a hot dull knife across its surface in a wave pattern (dip the knife in hot water and wipe completely dry before using it).
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17
Lightly dust the top of the cake with sifted cocoa powder.
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18
Allow the cake to stand at room temperature for 45 minutes before serving.
