FOR THE SAUCE: Mix the sugar and the 1/4 cup water together in a heavy saucepan, bring to a boil over medium-high heat, and boil, uncovered, for 6 to 7 minutes, until the mixture becomes a dark blond caramel. Pour about 1/4 cup of the caramel into a 4- to 5-cup soufflé dish, and tilt the dish so the caramel coats the bottom. (There should be just enough caramel to cover the bottom of the dish.)
Slowly add the 1/3 cup water to the caramel remaining in the pan, so as to prevent splattering. When all the water has been added, bring back to a boil and mix well with a wooden spoon. All the caramel should have melted, with no thick layer underneath that has stuck to the bottom of the pan. If necessary, keep stirring until this layer is dissolved. Transfer the liquid caramel sauce to a bowl and let cool; it will thicken to the consistency of a heavy syrup.
When the caramel is cool, add the cognac or Armagnac and lemon juice and stir well. Set aside. (The sauce can be made ahead and refrigerated in a jar with a tight-fitting lid for several months; bring to room temperature before serving.)
Preheat the oven to 350 degrees.
FOR THE CUSTARD: Mix the eggs, egg yolk, vanilla, and sugar in a bowl with a whisk. Add the milk and cream and mix until it is incorporated. Strain the mixture into the caramel-lined soufflé dish, and place the dish in a large saucepan or a baking pan. Add enough water to the saucepan so that it covers about halfway up the sides of the soufflé dish.
Bake for 45 to 55 minutes, until the custard is set in the center. To check, insert the tip of a paring knife into the center of the custard; if the blade comes out clean, the custard is set, although it may still look and feel soft in the center.
Remove the dish from the water and let cool, then refrigerate for at least 5 hours, or, preferably overnight.
To unmold the flan, run a sharp knife around the edges of the dish, making sure that the knife does not cut into the flan. Place a platter on top of the flan and invert it, moving the dish gently to dislodge the custard. Some liquid will come out of the dish as the flan dislodges; discard this thin caramel, and pour some of the thick caramel-cognac sauce over the custard.
Serve the flan with the remaining caramel-cognac sauce.
Copyright © 2011 by Jacques Pépin. Used by permission of Houghton Mifflin Harcourt. All rights reserved.
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