Vanilla-Bourbon Pudding Cake

The cake can be made in any of the following: six 3⁄4-cup custard cups, four 1-1⁄3-cup ramekins or miniature soufflé cups, one 9-inch round cake pan, or one 8-inch square cake pan. All pudding cakes, regardless of pan size, require the same baking time.

1. FOR THE CAKE: Adjust oven rack to middle position and heat oven to 325 degrees. Grease pan or baking molds of choice. Lay folded kitchen towel in bottom of roasting pan and set molds or pan inside. Bring kettle of water to boil.
2. Meanwhile, using back of wooden spoon, mash butter, sugar, and salt together in medium bowl until crumbly. Beat in egg yolks, then stir in flour, mixing until smooth. Slowly beat in vanilla and bourbon, then stir in milk. Using stand mixer fitted with whisk, whip egg whites and cream of tartar on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip until stiff peaks form, 3 to 4 minutes. Gently whisk whites into batter by hand just until no large lumps remain.
3. Immediately ladle (do not pour) batter into pan or baking molds of choice. Set roasting pan on oven rack. Quickly pour enough boiling water into roasting pan to come halfway up sides of pan or molds. Bake cake until center is set and springs back when gently touched, about 25 minutes. Remove roasting pan from oven and let pan or molds continue to sit in water bath for 10 minutes.
4. FOR THE SAUCE: Meanwhile, cook butter, sugar, bourbon, water, nutmeg, and salt in small saucepan over medium-low heat stirring occasionally, until bubbly around the edges. Off heat, whisk in egg. Return to medium-low heat and, stirring constantly, bring to boil and cook until thickened, about 1 minute. Spoon sauce over each cake and serve warm, passing remaining sauce separately.