In a 10-inch cast iron skillet, add butter and peaches. Cook over medium heat. Gently toss peaches until they begin to release their juices.
Add lemon juice, salt, cinnamon, and allspice to the peaches. Toss until well combined. In a small bowl, combine sugar and cornstarch. Pour over the peaches and gently stir. Remove from heat and set aside.
Preheat oven to 375°F.
In a medium bowl, whisk together flour, sugar, baking powder, baking soda, and salt. Using a pastry blender, cut the cold butter into the flour until the mixture resembles a coarse meal. Add cold buttercream and mix until a dough forms.
Using a large spoon, gently drop portions of dough on top of the peaches. Avoid completely covering the skillet. Brush the top of the dough with heavy cream and sprinkle turbinado sugar on top.
Line a baking sheet with parchment paper and place the skillet on top. Bake for 35-40 minutes until golden brown. Allow the cobbler to cool for 20 minutes before serving.