Preheat oven to 350 degrees F and grease a 2-quart baking dish with non-stick spray.
Spread sliced peaches evenly into the prepared baking dish and sprinkle with 2 tablespoons sugar.
In a medium bowl, beat softened butter and 1 cup sugar together until creamy.
Add flour, baking powder, salt, and optional nutmeg, then mix until combined.
Add egg and vanilla extract and continue mixing until a soft cookie-style batter forms.
Flatten small pieces of dough with your hands and place them over the peaches without fully covering the fruit.
Bake for 36 to 40 minutes until the topping is golden brown and cooked through.
Let the cobbler rest for 5 to 10 minutes before serving warm with vanilla ice cream or whipped cream.
