Preheat oven to 375 degrees F. Combine peaches, bourbon, 1/4 cup of the sugar, cornstarch, and cinnamon in a large bowl. Mix well to coat the peaches evenly.

Prepare the topping by sifting together the flour, the remaining 1/2 cup sugar, baking powder, and salt into a large bowl. Cut 1 1/2 sticks (12 tablespoons) of the butter into small pieces. Add it to the flour mixture and cut it in with a pastry blender until the mixture looks like coarse bread crumbs. Pour in the cream and mix just until the dough comes together. Don't overwork; the dough should be slightly sticky but manageable.

Melt the remaining 4 tablespoons of butter in a 10-inch cast-iron skillet placed over medium-low heat. Add the peach mixture and cook gently until heated through, about 5 minutes. Transfer peach mixture to a 2-quart baking dish (or, if desired, leave mixture in cast-iron skillet). Drop the dough by tablespoonfuls over the warm peaches(There can be gaps because the dough will puff up and spread out as it bakes.) Brush the top with a small amount of heavy cream and sprinkle with some sugar and a little extra cinnamon. Bake in the preheated oven on a tray (to catch any drips) for 40 to 45 minutes, until the top is brown and the fruit is bubbling. Serve warm with vanilla bean ice cream.