Heat the oven to 325 degrees. Line the bottom of an 8-inch springform pan with parchment paper and very generously grease the sides of the pan. Wrap the outside of the pan with 2 sheets of heavy-duty aluminum foil and set it in a large roasting pan. Bring a kettle or pot of water to boil.
In a stand mixer using the whisk attachment, beat eggs at high speed until they double in volume (approximately 5 minutes).
While the eggs are whisking, melt the chocolate and butter together by placing a large heatproof bowl over a pan of almost-simmering water. Keep bowl over simmering water until butter and chocolate mixture is smooth and very warm – about 115 degrees on an instant-read thermometer. Stirring occasionally. Remove from heat, and stir in almond extract.
Fold about a third of the beaten eggs into the chocolate mixture using a large rubber spatula until only a few streaks of egg are visible. Fold in half of the remaining egg foam, and then the last half of the foam, until the mixture is totally homogenous.
Spoon the batter into the prepared springform pan and smooth the surface with a rubber spatula. Place the roasting pan on the oven rack and pour in enough boiling water to come about halfway up the sides of the springform pan. Bake until the cake has risen slightly, the edges are just beginning to set, a thin-glazed crust (like a brownie) has formed on the surface, and an instant-read thermometer inserted halfway into the center reads 140° F, 22-25 minutes. Remove the springform pan from the water bath and set on a wire rack; cool to room temperature. Cover and refrigerate overnight to mellow and firm.
About 30 minutes prior to serving, carefully remove the sides of the springform pan, invert the cake onto a sheet of waxed paper, peel off the parchment paper, and reinvert the cake onto a serving platter. Lightly dust the top of the cake with powdered sugar.