Step 1: Make the Peach Filling
In a saucepan over medium heat, cook the diced peaches, butter, brown sugar, white sugar, cinnamon, nutmeg, salt, and lemon juice until the peaches are tender. Stir in the cornstarch and water mixture to thicken. Remove from heat and cool completely.
Step 2: Make and Rise the Dough
In a large bowl, combine the sourdough discard, warm milk, yeast, sugar, eggs, vanilla, kosher salt, softened butter, and bread flour. Mix and knead for 8 to 10 minutes until smooth and elastic. Cover and let rise in a warm spot until doubled in size.
Step 3: Mix the Cinnamon Filling
In a small bowl, thoroughly mix together the softened butter, brown sugar, cinnamon, vanilla, and kosher salt until it forms a spreadable paste.
Step 4: Assemble the Rolls
Roll the risen dough out onto a lightly floured surface into an 18x14-inch rectangle. Spread the cinnamon filling evenly across the dough, then top with the cooled peach filling (making sure to reserve a few spoonfuls for the final topping).
Step 5: Cut and Arrange
Roll the dough up tightly into a log, then cut it into 10 large bakery-sized rolls. Place the rolls into a buttered, parchment-lined 12-inch cast iron skillet.
Step 6: Second Rise and Cream Pour
Cover the skillet and let the rolls rise for 45 to 60 minutes. While they rise, pour ½ cup of warm heavy cream over and around the puffed rolls.
Step 7: Bake
Bake in a preheated 350°F (175°C) oven for 30 to 35 minutes until golden brown and cooked through.
Step 8: Frost and Finish
In a bowl, beat the cream cheese, butter, powdered sugar, vanilla, and salt until smooth. Spread the frosting over the warm rolls. Top with the reserved peach compote chunks and a generous sprinkling of a separately baked crumble topping to maintain that crisp cobbler texture.