Preheat the oven to 350F and place a rack in the lower third of the oven. Grease a 10-inch oven safe skillet or a 9x9 inch pan with nonstick cooking spray.
Add the fresh blackberries to a large bowl with the lemon zest, lemon juice, cornstarch, granulated sugar, ground cardamom and salt. Stir to combine and then let sit for 5-10 minutes while the oven preheats.
For the crumble topping, add the brown sugar, ground cardamom, all purpose flour and small cubes of butter to a medium bowl. Use your hands to rub all the ingredients together, breaking down the butter cubes, until it resembles a coarse meal, about pea-sized pieces. Add the pistachios and squeeze together the crumble with your hands to combine.
Transfer fresh blackberries and all of the juices from their bowl to the prepared baking dish. Use your hands to scatter the crumble topping over the blackberries.
Bake the crumble until the blackberry juices are bubbling around the edges and the top is golden brown, about 35-45 minutes. Let it cool slightly before serving scoops of the crumble with ice cream or whipped cream.