In a medium saucepan, combine 1 cup of the sugar with 1/4 cup of water, tilting the pot so that the water is evenly distributed. Cook over high heat, swirling the pan (but never stirring) until the sugar melts and turns to a deep amber color, 4 to 6 minutes. Immediately remove from the heat and, working very quickly, pour the caramel into a 2-quart porcelain casserole dish. Swirl the caramel to completely cover the bottom and partly up the sides of the casserole. Set aside to cool completely.
Preheat the oven to 350 degrees F.
Combine the milk, remaining 3/4 cup of sugar, orange zest, lime zest, and vanilla bean in a medium saucepan and bring mixture just to a boil. Cover pot and allow mixture to steep for 15 to 20 minutes.
In a medium mixing bowl, combine the eggs and egg yolks and whisk to combine. Add the hot milk mixture, little by little, and whisk lightly to combine. Strain the egg-milk mixture through a fine-mesh sieve into the caramel-lined casserole. Place the casserole in a larger baking dish or roasting pan and add enough hot water to come halfway up the sides of the casserole. Lay a piece of aluminum foil over the pan so that it is lightly covered and bake, undisturbed, until custard is just set, about 1 hour. (The timing may vary slightly depending on the baking dish used.) Remove the flan from the oven and transfer to a wire rack to cool. Cool completely and transfer to the refrigerator and chill, preferably overnight.
When ready to serve, run a sharp paring knife around the edge of the custard and shake the custard slightly to loosen. Invert an appropriately sized platter or serving dish over the casserole dish and, working quickly and holding both the casserole and the platter together, turn the casserole over and place the platter on a flat work surface. Gently lift the casserole off of the platter; the custard should gently fall from the casserole onto the platter. If not, tap the casserole and platter lightly on the work surface to help dislodge the custard. Let sit at room temperature for 15 minutes to warm slightly before serving. Serve slices of the flan with some of the caramel sauce spooned over top.
Cook's Note: Flan is best served cool or at room temperature and is more readily turned out