Preheat the oven to 350 F. Line a small baking sheet with parchment paper.
In a food processor, add the pistachios, all-purpose flour, almond flour, brown sugar, kosher salt and pulse until combined and the pistachios are roughly chopped. Add the melted butter and pulse again to combine.
Lightly grease a 2-quart baking dish and place the peach halves, cut side up in the dish (use a larger dish if necessary to fit all the peaches). Sprinkle half of the pistachio crumble over the peaches, and spread the remaining crumble on the prepared baking sheet in an even layer.
Transfer both the baking dish and baking sheet to the oven on the same or separate racks.
After 10 minutes of baking, flip the crumble and bake until it is golden brown (another 5-10 minutes), then remove to cool. The peaches may need a few more minutes to cook through depending on their ripeness.
Serve peach halves warm with vanilla ice cream and additional pistachio crumble to taste.
Video
Notes
*Nutrition information does not include ice cream. Calculations also assume that about 2/3 of the crumble will be used (I usually have some leftover).