Preheat the Oven: Heat your oven to 425°F.
Prepare the Skillet: Place a 10-inch oven-safe skillet over medium heat and melt the butter until it turns a light golden brown, which should take about 3 to 5 minutes. Once browned, take the skillet off the heat.
Mix the Filling: In a large mixing bowl, combine the peach slices with the brown sugar, flour, bourbon, vanilla extract, lemon juice, cinnamon, ginger, and salt. Toss everything together until the peaches are evenly coated. Pour this mixture into the skillet and stir it gently to combine with the melted butter.
Add the Puff Pastry: Lay the thawed puff pastry sheet over the peach mixture, gently pressing it down to fit. Tuck any overhanging edges of the pastry under the peaches where possible. Brush the pastry with the beaten egg and sprinkle coarse sugar over the top for extra texture.
First Bake: Place the skillet on a baking sheet (to catch any drips) and bake for about 20 minutes, or until the pastry is puffed and golden brown.
Cut and Adjust the Pastry: Remove the skillet from the oven and carefully cut the pastry into large squares with a sharp knife, creating a crosshatch design. Lower the oven temperature to 350°F.
Add Cream and Finish Baking: Spoon the heavy cream over the pastry and return the skillet to the oven. Bake for an additional 20 minutes, or until the pastry is a deep golden color and the peach juices are bubbling up through the cracks in the pastry. If the pastry starts to brown too much, you can loosely cover the skillet with aluminum foil.
Final Touches: Once baked, use a spoon to gently press the pastry down into the bubbling juices without fully submerging it. Serve the pandowdy warm, and if desired, pair it with vanilla ice cream for an extra indulgent treat.