Preheat the oven to 375°F (190°C). In a large bowl, add the peaches, bourbon, 1/4 cup of sugar, cornstarch, and cinnamon, and mix well to coat the peaches evenly. Set aside.
Prepare the dumplings: In a food processor, add the flour, 1/2 cup of sugar, baking powder, and salt. Cut 1 1/2 sticks of butter into small pieces and add them to the flour mixture. Pulse until the mixture resembles wet sand.
Pour in the cream and mix just until the dough comes together. Don’t overwork it; the dough should be slightly sticky but manageable.
In a 10-inch (25cm) cast-iron skillet over medium-low heat, melt the remaining 1/2 stick of butter. Add the peaches and cook gently until heated through, about 5 minutes. Transfer the mixture to a baking dish (or leave it in the skillet). Drop the dough by tablespoonfuls over the warm peaches. It’s fine if there are gaps; the dough will puff up and spread out as it bakes.
Brush the top with heavy cream and sprinkle with sugar. Place it on a baking sheet to catch any drips, and bake for 40 to 45 minutes, until the top is browned and the fruit is bubbling.