Combine peaches, sugar, flour and nutmeg in a Dutch-oven. Set aside until a syrup starts to form (~3 minutes).
Heat peach mixture over medium-low heat until it starts to boil. Reduce heat to low and cook peaches for approximately 10 minutes or until peaches are tender. Remove peaches from heat and stir in vanilla and butter.
Preheat oven to 450°F. Spray a deep square baking dish with non-stick cooking spray. Spoon peaches into pan.
Roll pastry to ⅛” thickness and cut into 1” wide strips. Arrange in a lattice design over peaches. Bake for 12-15 minutes, or until crust is lightly browned. Let cool slightly before serving.