Preheat the oven to 375℉. In a large bowl, combine the sliced peaches, brown sugar, flour, lemon juice, cinnamon and nutmeg. Toss to coat.
For the Crumble Topping
In a medium bowl, combine flour, sugar, baking powder, salt, and cinnamon. Stir in the egg until the mixture resembles coarse crumbles.
Assemble and Bake
Transfer peaches into a greased, shallow 2½ quart oven-proof baking dish. Sprinkle crumble topping over the peaches and then pour melted butter evenly over the topping.
Bake for 35 to 40 minutes.
Salted Caramel Sauce
In a medium saucepan over medium-high heat, combine the sugar with ¼ cup cold water and stir. Then, cook, without stirring, until the sugar has turned a deep amber hue, approximately 10 to 12 minutes.
Meanwhile, warm the cream in a small saucepan. When the caramel is ready, slowly whisk in the warm cream and continue simmering the mixture until it is smooth, another 2 to 3 minutes. Remove from heat, then whisk in the butter, and then the salt, to taste. Serve warm.
Notes
Peaches: If using frozen peach slices, be sure to thaw and drain any remaining moisture.