How to Make It
Preheat the oven to 250°. Butter eight 4-ounce ramekins and sprinkle them with sugar. In a large bowl, beat the cream cheese with the sugar until smooth. In a medium bowl, beat the eggs with the lemon juice and rum. Gradually beat the eggs into the cream cheese. Strain into a large measuring cup.
Pour the lemon mixture into the prepared ramekins. Set the ramekins in a baking dish and add enough hot water to the dish to reach halfway up the sides of the ramekins. Bake for about 1 hour, or until the flans are set. Let cool in the water bath for about 21/2 hours. Raise the oven temperature to 325°.
In a heavy, medium, nonreactive saucepan, combine the egg yolks, sugar, and lemon juice. Whisk over low heat until slightly thickened, about 5 minutes; do not let boil. Remove from the heat and stir in the rum. Pour the sauce into a medium bowl, set it in a larger bowl of ice water and let cool, stirring occasionally. As the mixture cools, gradually stir in 2 to 3 tablespoons of cold water until the sauce has a pourable consistency.
Using a lemon zester, strip the zest from the lemons. In a small saucepan of boiling water, blanch the zest for 1 minute; drain. Repeat the blanching process two more times to remove the bitterness. Transfer the zest to paper towels and pat dry.
In a heavy medium saucepan, combine 1 cup of the sugar with 1/4 cup of water. Stir over moderate heat to dissolve the sugar, then boil the syrup until it reaches 238° on a candy thermometer, about 7 minutes. Remove from the heat and stir in the lemon zest. Drain the zest and transfer to a bowl. Toss the zest with the remaining 1/2 cup sugar until coated.
Line a small baking sheet with parchment paper. In a small saucepan, melt the butter over low heat. Pour the butter into a small bowl, leaving the milky residue behind.
Spread 1 sheet of the phyllo dough on a work surface; keep the remaining sheets covered with a damp towel. Lightly brush the phyllo with the melted butter. Lay another sheet of phyllo on top and brush with butter. Repeat the process with the remaining phyllo and butter.
In a small bowl, combine the sugar and cinnamon. Using a 3-inch round pastry cutter or a glass, cut out 8 circles from the phyllo dough and transfer them to the prepared baking sheet. Sprinkle the circles with the cinnamon sugar and cover with another sheet of parchment. Bake for about 25 minutes until crisp and golden. Remove the top layer of parchment and let cool on the baking sheet for up to 2 hours.
Run a knife around the inside of each ramekin and invert each flan onto a plate. Top with a pastry crisp, sugared side up. Spoon the lemon sauce around the flans and garnish with the candied zest and mint leaves.