Preheat oven to 375 degrees. If using frozen cherries, spread them in a single layer on a rimmed baking sheet. Let stand at room temperature until cherries have thawed almost completely but still hold their shape, about 30 minutes. Drain off any accumulated liquid.
Whisk together the pistachios, flour, oats, baking powder, and 1/4 teaspoon salt in a medium bowl; set aside. Put butter, brown sugar, and 1/4 cup granulated sugar in the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until creamy.
Stir pistachio mixture into butter mixture until just combined. Work mixture through your fingers until it forms coarse crumbs ranging in size from small peas to gum balls; set topping aside.
Stir together cherries, remaining 1/2 cup granulated sugar, the cornstarch, cinnamon, and a pinch of salt in a medium bowl. Transfer cherry mixture to an 8-inch square baking dish. Sprinkle the topping evenly over cherry mixture. Bake until topping turns golden and juices are bubbling, 50 minutes to 1 hour. Let cool on a wire rack 1 hour before serving.