Prepare the peaches by scoring an x on the bottom of the peaches and placing them into boiling water for ten (10) minutes. Remove the peaches with a large slotted spoon and put them in a cool water bowl. When the peaches have cooled enough to safely handle, remove their skins, cut them in half, and remove the pit. Continue to slice the peaches into roughly 3/4 inch thickness. Continue until all of the peaches are sliced.
Place peaches into a large mixing bowl.
Into a smaller mixing bowl, add the sugar, light brown sugar, salt, lemon juice, balsamic vinegar, vanilla extract, ground cinnamon, and ground cardamom, and mix well.  
Pour the mixture over the peaches and fold gently to coat the peaches evenly. Allow the peaches to steep for ten (10) minutes. 
Lay your chilled crust over the cast iron skillet (or onto a baking sheet) and tuck in the edges.
Pour or spoon the peaches into the center of the pie dough and fold/overlap the dough completely around the diameter of the skillet. 
Brush the pie dough with egg wash, get into all those nooks and crannies, and dot the top of the pie with several cubes of unsalted butter. 
Dot the top of the galette with cubes of chilled unsalted butter. 
Place the galette onto the center rack of a preheated 375° oven and bake for twenty (20) to twenty-five (25) minutes. 
Remove the galette from the oven, and serve warm. 
Pair the galette with vanilla ice cream or whipped cream.