How to Make It
Bring a large saucepan of water to a boil and fill a bowl with ice water. Score a shallow X in the bottom of each peach. Submerge the peaches in the boiling water for 1 minute. Using a slotted spoon, transfer the peaches to the ice water to cool. Peel the peaches, cut them into eighths and transfer them to a heatproof bowl.
Rinse out the saucepan. Add 2 cups of the sugar, the lime and lemon zests, the lemon juice and 2 cups of water and bring to a boil, stirring until the sugar is dissolved. Pour the hot syrup over the peaches, then top them with a small plate to keep them submerged in the syrup. Refrigerate until chilled, at least 4 hours.
Meanwhile, rinse out the saucepan and add 4 cups of the milk, the vanilla bean and seeds and 1/4 cup of the sugar. Bring to a boil, stirring until the sugar is dissolved. Stir in the rice and a pinch of salt and cook over moderately low heat, stirring constantly, until the rice is tender and the liquid is very thick and nearly absorbed, about 35 minutes. Remove from the heat and discard the vanilla bean.
In a medium saucepan, combine 2/3 cup of water with the butter and 1/4 teaspoon of salt; bring to a boil. Off the heat, stir in the flour with a wooden spoon. Return the saucepan to moderate heat and cook, stirring, for 1 minute. Using an electric mixer at medium speed and working off the heat, beat in the eggs one at a time, beating well between additions. Transfer the dough to a pastry bag fitted with a 1/2-inch star tip.
Fill a large saucepan with 3 inches of oil and heat to 375°. Line a rack with paper towels. In a bowl, combine the remaining 1 cup of sugar with the cinnamon and a generous pinch of salt. Carefully squeeze the batter into the hot oil in 3-inch lengths, using a knife or kitchen scissors to cut the churros as they gently fall into the oil; fry no more than 8 at a time. Fry the churros over high heat, turning once, until golden brown, about 3 minutes per batch. Using a slotted spoon, transfer the churros to the rack to drain for 30 seconds, then immediately toss them in the cinnamon sugar to coat. Continue frying the churros, coating them as they are done.
Using a slotted spoon, transfer the peaches to large glasses; top with 2 tablespoons of the syrup. Stir the remaining 1/2 cup of milk into the rice pudding and rewarm until hot, about 1 minute. Spoon the rice pudding over the peaches and serve with the churros.