



Mix together the flour, 2 tablespoons of sugar, and a pinch of salt in a large bowl. Transfer to an airtight container and freeze until firm, about 4 hours. Pour mixture into an ice cream maker and freeze according to manufacturer's instructions, about 20 minutes. Mixture will be really thick, so working it through with a silicone spatula can take up to 10 minutes as you press and stir. Whisk in egg yolk mixture and return to low heat, whisking constantly, until a custard forms, 5 to 10 minutes. Remove milk from heat and allow to cool to 170 degrees F (76 degrees C). Add more hot milk slowly to temper the mixture. Slowly whisk 1/2 cup of the hot milk mixture into the egg yolk mixture. Use an immersion blender to puree the peaches and the milk. Remove vanilla bean and scrape the seeds into the hot milk. Stir to combine and simmer for about 10 minutes. Add peeled peaches and all the caramelized juices into the hot milk. When peaches are done, remove skins (and eat them, they're delicious!). Whisk together egg yolks, white sugar, cornstarch, and vanilla extract in a bowl until well combined. Meanwhile, heat milk and split vanilla bean in a large pan over medium heat, stirring to avoid any burning. Cover the pan with foil and continue to bake until peaches are fully cooked and sugar is mixed with butter and juices form a caramel in the pan, about 15 more minutes. Turn peaches over with a spatula and sprinkle brown sugar and cinnamon into the juicy halves. Bake in the preheated oven until mostly cooked and bubbly, about 20 minutes. Generously butter the cut portion of each peach half and place cut-side down into a baking pan. Preheat the oven to 400 degrees F (200 degrees C).
