Butter an 8-inch-square pan and line with parchment paper. Press half of a 16-to-18-ounce package refrigerated sugar cookie dough into the bottom of the pan and bake at 375 degrees F, 8 minutes. Toss 1 1/2 cups sliced peaches with 2 tablespoons brown sugar, 1 teaspoon ground ginger and a pinch of salt; arrange on the crust. Increase the oven to 425 degrees F and bake until golden, 10 to 12 minutes. Sprinkle with cinnamon sugar.