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1
Preheat the oven to 425*F.
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2
Butter a 9-inch square baking pan, line it with foil, and butter the foil.
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3
Set the eggs in a bowl and cover them with hot tap water.
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4
Over very low heat, melt the chocolate with the butter, stirring until smooth. Stir in the vanilla. Transfer the mixture to a bowl and let it cool slightly on a wire rack.
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5
Put the warm eggs in a large bowl and beat with an electric mixer on high speed until about tripled in volume, about 5 minutes. Fold half the beaten eggs into the chocolate mixture to lighten it. Gently fold in the remaining beaten eggs. Scrape the batter into the prepared pan and smooth the top.
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6
Set the brownie pan in a larger baking pan. Pour hot water into the larger pan to come halfway up the sides of the brownie pan.
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7
Bake the brownies on the middle oven rack for 10 minutes. Shut the oven and let the brownies stand inside for 5 minutes. Remove the brownies from the water bath to a wire rack and let stand while preparing the glaze.
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8
Glaze: Heat the cream with the chocolate, stirring until smooth.
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9
Pour the hot glaze evenly over the surface of the brownies; spread smooth with a thin spatula and let cool completely.
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10
When cool, cover the pan with plastic wrap and refrigerate until well chilled and firm, at least 4 hours, or overnight.
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11
To serve, cut into 12 squares. Arrange the brownies on a serving plate. For best flavor and texture, allow the brownies to come to room temperature before eating.