Pre-heat the oven to 400°F.
Roll the pie crust out into a big circle; about 12-inches in diameter; don’t worry if it’s not a perfect circle.
Transfer the pie crust onto a rimmed baking sheet; keep in the freezer or refrigerator while working on the peaches.
Cut the peaches into quarters; then cut the quarters into quarters; for a total of 16 slices per peach; discard the pits.
Toss the peaches in a big mixing bowl with the brown sugar, cinnamon, spiced rum, vanilla extract, lemon juice and flour; set this mixture aside.
Dump the peaches, along with any of the liquid in the bowl, onto the center of the rolled out pie crust, leaving a 2-inch rim on all sides of the peaches
Distribute the peaches as necessary to form into a relatively flat layer; it’s okay to have the peaches piled up on top of each other.
Gently fold the sides of the pie crust up and over the peaches; brush the crust with heavy cream.
Sprinkle turbinado sugar all over the heavy cream brushed pie crust.
Place in pre-heated oven and bake the crostata for about 40 minutes until the edges are golden brown and the peaches are bubbling.
Serve warm with a big scoop of vanilla ice cream, if desired.
