3medium peaches1 pitted and chopped, 2 cut into 1/4-inch wedges, about 500g total
1/2cupplus 1 teaspoon fresh lime juice
5tablespoonschilled unsalted buttercut into pieces
Preheat oven to 90°C. Using a stand mixer fitted with the whisk attachment, beat egg whites on medium-high speed until frothy, about 1 minute. With the motor running, add 1/2 cup sugar, 1 Tbsp. at a time, and beat until medium peaks form, about 5 minutes. Continue to beat until stiff, glossy peaks form, 10–12 minutes.
Transfer meringue to pastry bag and cut off tip so opening is 1/4″ wide. Pipe four 3 1/4″ rounds onto a grease proof-lined rimmed baking sheet. Bake meringues until dry, firm, and peel easily off of baking sheet around 90–105 minutes. Turn off oven and let cool in oven with door slightly ajar.
Meanwhile, pulse chopped peach in a food processor until smooth. Transfer peach purée to a small bowl.
Toss peach wedges with 1 Tbsp. sugar and 1 tsp. lime juice. Let sit, tossing occasionally, until peaches release their juices.
Bring a medium pot of water to a simmer. Whisk rum, egg yolks, and remaining 1/3 cup sugar and 1/4 cup lime juice in a medium bowl. Place bowl over a pot of barely simmering water and cook, whisking constantly, until mixture is foamy and thickens slightly, around 5 – 6 minutes. Whisk in butter a few pieces at a time, incorporating completely before adding more. Stir in peach purée and let cool slightly.
Strain through a fine-sieve into a small bowl. Press plastic wrap directly onto surface and chill until cold, at least 2 hours.
Gently break each meringue and divide among bowls. Spoon peach curd over and top with macerated peaches.
Do Ahead: Peach curd can be made 2 days ahead. Cover and chill.