Activate the Yeast: Heat milk to 100–110°F. Stir in the yeast and let sit 5–10 minutes until bubbly and foamy.
Make the Dough: In a stand mixer, combine the milk mixture with sugar and egg. Add flour and salt and knead for 5 minutes. Add cubed butter, one tablespoon at a time, and knead for another 5 minutes. Cover the bowl and let the dough rise for 1–2 hours until doubled in size.
Shape the Buns: Punch down the dough and divide into 6 equal portions. Roll each into a ball and flatten slightly. Press the center down and push the sides outward to form a 'bowl' or divot in the middle (5–6 inches wide). Place on parchment-lined sheet and brush edges with egg wash.
Make the Cream Cheese Custard: Beat the cream cheese until smooth. Add vanilla and heavy cream, mix well. Slowly add powdered sugar and beat until light and fluffy. Pipe into the center of each bun.
Drizzle Salted Caramel: Drizzle half of the salted caramel on top of the custard filling.
Prepare the Peaches: Toss diced peaches with brown sugar, flour, and cinnamon. Spoon over the caramel in each bun.
Add the Crumble: Combine melted butter, flour, brown sugar, and vanilla. Sprinkle crumble on the outer edges of each bun.
Bake: Bake at 375°F for 20–25 minutes, until golden and set.
Cool and Finish: Let cool for 15 minutes undisturbed to allow the custard to set. Drizzle with salted caramel or desired topping.
