Heat oven to 375°F. Slice 1/2 stick butter into a 10-inch cast iron skillet and set aside.
Peel and slice the peaches into a bowl.
Melt the skillet butter in the oven for a few minutes, just until melted (not browned).
Toss the peaches with brown sugar, cornstarch, cinnamon, and vanilla, stirring gently.
Pour peaches into the buttered skillet and bake 7 to 10 minutes.
In a bowl, stir together flour, brown sugar, kosher salt, baking powder, and nutmeg. Grate in the cold butter, sprinkle with a little of the flour mixture, and stir to coarse crumbles.
Stir in the milk and heavy cream until just combined into a thick batter (add a touch more milk if needed). Do not overmix.
Dollop the topping over the pre-baked peaches with lightly greased hands, filling in any bare spots.
Brush the topping with heavy cream. Mix the turbinado sugar with a pinch of cinnamon and sprinkle over the top.
Bake at 375°F for 40 to 45 minutes. Tent loosely with foil if the top browns too quickly, removing it for the last 3 to 4 minutes.
Rest 15 minutes before serving. Serve warm with vanilla ice cream.