Step 1In a medium bowl combine the sugars, flour, oats, cornmeal, ginger and chopped pistachios. Using your fingertips, work in the melted butter until you have a coarse crumbly texture. Do not mix with a spoon.
Step 1Cut the peaches in half and remove the pits. Thinly slice each half. Make six circles by fanning the slices of each peach half and place in a shallow 9- by 12-inch glass baking dish. The circles will cover most of the bottom of the dish.
Step 2Place 3 quartered cherries in the center of each peach circle. Drizzle 1 tablespoon of melted butter over the top of each circle and sprinkle each with 1 teaspoon of granulated sugar.
Step 3Sprinkle the crisp topping over the fruit, being sure to cover peaches and cherries evenly.
Step 4Bake at 350 degrees for 35 to 40 minutes until the center of the crisp begins to bubble and the juices begin to emerge through the golden-brown topping. Remove the crisp from the oven to a wire rack to cool. Let stand about 10 minutes to cool.
Step 5Cut the crisp into 6 squares, each with a fanned peach circle. Use a wide spatula to lift the squares to serving plates. Serve with a scoop of pistachio ice cream.