Position an oven rack on the middle rung and heat the oven to 350°F.
Butter a 9x3-inch round cake pan. Line the bottom of the pan with a round of parchment and butter the parchment. Set the cake pan in a roasting pan large enough to accommodate it.
Melt the chocolate and butter over a double boiler. Remove from the heat and let cool slightly.
With an electric mixer (a stand mixer with the whip attachment or a hand mixer), beat the egg yolks with the brown sugar on medium speed until very pale, thick, and fluffy, about 3 minutes. Reduce the speed, add the chocolate mixture, and mix just to combine. Add the flour, mixing just to combine and scraping the bowl as needed. Blend in the bourbon and vanilla. Transfer to a large mixing bowl and set aside.
In a clean mixing bowl with clean beaters, beat the egg whites with the salt on high speed until they hold soft peaks, 1 to 2 minutes. With a rubber spatula, fold one-third of the egg whites into the chocolate mixture to lighten it, and then gently fold in the remaining whites. Scrape the batter into the prepared cake pan.
Set the roasting pan on the oven rack and add enough warm tap water to come halfway up the sides of the cake pan. Bake until the top feels set, 40 to 45 minutes. Remove the cake pan from the water bath and run a paring knife around the inside of the pan (or the inside of the parchment collar) to loosen the cake and then let the cake cool completely in the cake pan on a rack. When the cake is completely cool, loosen the sides once more with a paring knife. Cover the cake with a serving plate and invert the cake onto the plate. The bottom of the cake is now the top. Peel off the parchment. (Don’t worry if the surface looks a little ragged; you’ll be dusting with confectioners’ sugar).
To serve: In a chilled bowl with chilled beaters, beat the cream and sugar to medium-soft peaks. Dust the top of the cake generously with confectioners’ sugar, slice, and serve each slice with the whipped cream.