Prepare the Peaches In a mixing bowl, combine sliced peaches with brown sugar, granulated sugar, cinnamon, and nutmeg. Toss the peaches until evenly coated, then set aside to let the flavors develop.
Prep the Donuts Cut the Krispy Kreme donuts into 1-inch cubes. Spread half of the cubed donuts at the bottom of a greased 9×13-inch baking dish.
Assemble the Cobbler Layers Pour half of the spiced peaches over the donut layer in the baking dish. Add the remaining donuts on top, followed by the rest of the peaches.
Add the Cream Mixture In a separate bowl, whisk together the heavy cream, melted butter, and vanilla extract. Pour this mixture evenly over the donut and peach layers. This helps soak the donuts, giving a custard-like texture as it bakes.
Bake the Cobbler Preheat your oven to 350°F (175°C) and bake the cobbler for about 30–35 minutes, or until the top is golden and the peaches are bubbling.
Serve Warm Let the cobbler cool slightly before serving. Serve warm, topped with a scoop of vanilla ice cream or a dollop of whipped cream if desired.