This silky peach-topped cheesecake is made with another Georgia staple: pecans. For the smoothest texture, make this gluten-free dessert a day in advance and store in the refrigerator before serving.
Place ricotta cheese in a cheesecloth-lined colander. Set colander in a bowl, and cover colander and bowl with plastic wrap. Chill 8 to 12 hours to drain.
Preheat oven to 350°F. Spread chopped pecans in a single layer on a rimmed baking sheet, and bake in preheated oven until fragrant and lightly toasted, about 10 minutes. Remove from oven, and cool on baking sheet 20 minutes. Process pecans in a food processor until finely ground. Transfer to a medium bowl. Add brown sugar, kosher salt, and 1 tablespoon of the tapioca starch; whisk to combine. Add beaten egg white, and whisk just until blended. Using dampened fingers, press pecan mixture onto bottom and up sides of a lightly greased 9-inch springform pan, making crust about 1/8 inch thick.
Place a large pan of water on the bottom rack of the oven. Transfer the drained ricotta to a food processor. Peel 1 peach, cut in half, and remove pit. Add peach to ricotta. Process 30 seconds; scrape down sides. Add cream cheese, granulated sugar, eggs, and remaining 2 tablespoons tapioca starch. Process 30 seconds; scrape down sides. Add lemon zest, vanilla extract, fine sea salt, almond extract, and 1 tablespoon of the lemon juice. Process until smooth, stopping occasionally to scrape down sides. Transfer batter to prepared crust, and place on the center rack of the oven, above the pan of water.
Bake in preheated oven until top puffs up and begins to brown and center of cheesecake seems mostly set (it will jiggle a little), about 1 hour and 10 minutes. Transfer cheesecake to a wire rack, and cool 4 hours (or cover and refrigerate overnight). The cheesecake will settle slightly as it cools.
Gently rub the 3 remaining peaches under running water to remove fuzz, and thinly slice peaches. Toss together peach slices and remaining 1 tablespoon lemon juice in a large bowl. Top cheesecake with sliced peaches, and garnish with fresh mint, if desired.