Preheat the oven to 300 degrees. Set two 10-inch deep-dish glass pie plates in 2 medium roasting pans.

In a saucepan, cook the sugar and water over moderately high heat, stirring just until the sugar dissolves. Using a wet pastry brush, wash down any crystals from the side of the pan. Cook the syrup undisturbed until a medium-amber caramel forms, 6 minutes. Immediately pour the caramel into the pie plates, tilting them to coat the bottoms. Let the caramel cool completely.

In a large bowl, whisk the eggs with the vanilla seeds, orange zest, and orange liqueur. Whisk in both milks until evenly combined. Pour the custard into the pie plates. Set the roasting pans on the upper- and lower-third oven shelves. Carefully pour enough hot water into each roasting pan until it reaches halfway up the side of the pie plate. Cover the roasting pans with foil and bake for 1 1/2 hours to 1 hour and 50 minutes (depending on oven placement), until the flans are firm and set but still slightly jiggly in the centers. Transfer the roasting pans to racks and let the flans cool slightly in the water. Transfer the pie plates to racks and let the flans cool, then cover, and refrigerate overnight.

Using a sharp knife, peel the oranges and limes, removing all of the bitter white pith. Working over a bowl, cut in between the membranes to release the sections. Cut each section in thirds and return them to the bowl. Add the melon, basil, olive oil, and salt.

To unmold each flan, run a knife around the rim of the pie plate, being sure to reach the caramel on the bottom; tilt the plate slightly to allow a bit of the caramel into the gap. Invert a rimmed round platter over the pie plate. Grabbing both, carefully invert the flan onto the platter; if it doesn't release immediately, lift one side of the pie plate about an inch and slip the tip of the knife between the glass and the flan to release the seal. Lift off the pie plate. Pour and scrape the caramel onto the flan. Cut into wedges and serve with the fruit salad.

The molded flans can be refrigerated for up to 3 days.