Heat the oven to 375 degrees F.
In a large bowl add the peaches, bourbon, 1/4 cup sugar, cornstarch, and cinnamon and mix well to coat the peaches evenly; set aside.
Prepare the dumplings: Into a bowl sift together the flour, 1/2 cup sugar, baking powder, and salt. Cut 12 tablespoons (1 1/2 sticks) butter into small pieces. Add it to the flour mixture and cut it in with a pastry blender or your hands 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.
In a 10-inch cast iron skillet over medium-low heat, melt the remaining 4 tablespoons butter. Add the peaches and cook gently until heated through, about 5 minutes. Drop the dough by tablespoonfuls over the warm peaches. There can be gaps, the dough will puff up and spread out as it bakes. Brush the top with some heavy cream and sprinkle with some sugar; put it into the oven on a baking sheet to catch any drips. Cook for 40 to 45 minutes until the top is browned and the fruit is bubbling.