Preheat oven to 350F. Butter and flour your 9" springform pan.
Finely chop your pistachios. I do this in my food processor, pulsing until they are finely ground but not reduced to a meal. Set aside.
Whip the cold cream until it forms firm peaks. Refrigerate.
Whisk together your flour, salt, and baking powder. Set aside.
Whisk eggs, sugar, and vanilla until really light and fluffy (I do this in my stand mixer.) Fold in the flour mixture, and the pistachios.
Gently fold the cream into the batter until there are no streaks left. Do this gently but thoroughly so you don't deflate the air you've whipped into the cream. Turn into your prepared pan and spread out evenly.
Bake for 50-60 minutes or until puffed and golden on top. A toothpick inserted in the center should come out without wet batter on it ~ but moist crumbs are fine. FYI my cake took closer to 60 minutes but your oven may bake differently.
Let the cake cool for ten minutes, then release from the pan. Transfer to a cake stand or serving plate and dust with powdered sugar. Top with more crushed pistachios.
The cake is wonderful warm or at room temperature. Store on the counter under a cake dome or loosely tented with foil. It will keep for several days.