Unlike many traditional cobblers, the thickener is cooked on the stove, then added to the peaches. The cobbler can be refrigerated after baking and single servings can be reheated in the microwave right before serving.
To make the cobbler: Preheat oven to 275 degrees. In a large bowl, add peaches and set aside. Spray an 8-by-8-inch baking pan with cooking spray. Fit one piecrust in pan securely, lining the sides 1 to 2 inches. Make sure to seal all tears in the dough. Bake for 10 minutes, until dough is soft and looks "melted." Remove pan from oven and set pan aside. Increase temperature to 350 degrees.
In a large saucepan off heat, mix cornstarch and cold water, stirring until smooth. Add peach brandy. Place over medium heat and whisk until thick and goes from white to translucent. The mixture will pull away from the sides and bottom of the pan. Add brown sugar, salt, cinnamon and nutmeg and whisk until completely smooth and sugar has dissolved. Remove from heat. The mixture will be very thick. Add mixture to peaches and combine gently. Pour peach mixture into cooked crust and cover with top crust. Press down lightly on top crust, tucking it around the filling, and carefully fit edges together for a complete seal. Don't worry if it doesn't look smooth, the mixture will be covered completely with the topping. Make sure there is about an inch of space left on top. If not, gently press the dough down. Bake for 1 hour, or until crust is golden brown.
To make the topping: About 15 minutes before the cobbler is ready, prepare topping. In a saucepan over low heat, combine butter and sugar and whisk until melted. Bring to a boil. Add water. The mixture will bubble wildly. Continue to whisk until smooth. When cobbler is done, remove topping from heat and fold in walnuts. Pour over top crust of cobbler.