For the topping: Combine the flour, brown sugar, cardamom and salt in a medium bowl. Work the butter into the dry ingredients using your hands until completely incorporated (it will be soft and slightly sticky). Stir in 3/4 cup pistachios and set aside.
For the filling: Toss the plums, granulated sugar, cornstarch, lemon juice and rose water, if using, together in a 3-quart baking dish. Scatter the topping over the plums, then scatter the remaining 1/4 cup chopped pistachios on top.
Bake until the fruit bubbles and the crumble is golden brown and crisped, 55 to 65 minutes. Let cool slightly before eating.