Place flour, sugar, and salt in a food processor and process for 5 seconds. Add butter and process until the mixture resembles coarse meal. Add water, a few tablespoons at a time, until the dough just comes together.
Remove dough and knead lightly on a lightly floured surface until it just comes together. Divide the dough in half and form into disks. Wrap each disk in plastic wrap and refrigerate for at least 30 minutes.
Once dough is chilled, remove from the refrigerator and roll each disk into a 9-inch square approximately 1/4-inch thick. Place on parchment paper-lined baking sheets and return to the refrigerator to chill until ready to assemble.
Melt butter in a large high-sided saute pan over medium heat. Add the sugar and water and cook until sugar is dissolved. Add nutmeg, salt, peaches, and flour and cook for 5 minutes.
Preheat oven to 375 degrees F.
Place half of the peach mixture in the bottom of a 9-inch square buttered baking dish using a slotted spoon. Top the peaches with 1 layer of dough. Place on a baking sheet and bake until the crust is light golden brown. Remove from the oven and top the crust with the remaining peaches and cover with the other crust. Brush the top crust with heavy cream, sprinkle with sugar, and return to the oven. Bake until the crust is golden brown and the juices are bubbly. Let cool for at least 30 minutes before cutting and serving.