Preheat a 10" Dutch oven to 350°.
Toss plums, lemon zest, lemon juice, cornstarch, ½ cup brown sugar, ½ tsp. salt, and ¼ tsp. cardamom in a large bowl; let sit until some juices accumulate, 5–10 minutes.
Meanwhile, use two knives to mix flour and remaining 1/3 cup brown sugar, ½ tsp. salt, and ½ tsp. cardamom in another bowl.
Add butter and mix with knives until mixture is very sandy and starts to form larger clumps.
Transfer plums and their juices to a the 10" Dutch oven, preferably lined with a disposable aluminum liner or parchment liner.
Scatter topping over fruit, squeezing small fistfuls in your hand to bring it together, then breaking into smaller pieces of varying sizes.
Sprinkle pistachios evenly over topping.
Refresh coals, roughly 13 on top, 7 below.
Bake crumble until juices are thickened and bubbling and top is golden brown, 40–45 minutes.
Let cool slightly.