Stone Fruit Custard Tart

1/2 cup (1 stick) unsalted butter
1/2 cup (65 g) raw pistachios, divided
1 large egg
1/4 cup (packed; 50 g) light brown sugar
2 cups (250 g) all-purpose flour
1 tsp. kosher salt
3/4 tsp. baking powder
Filling and assembly
3 large eggs
2/3 cup (packed; 133 g) light brown sugar
1/4 cup sour cream
1 Tbsp. vanilla bean paste or vanilla extract
1 tsp. ground cardamom
3/4 tsp. ground ginger
3/4 tsp.(packed) finely grated orange zest
3/4 tsp. kosher salt
3 Tbsp (23 g) all-purpose flour
2½–3 lb. stone fruit (such as peaches, nectarines, apricots, and plums; all about the same size), cut into sixths or eighths, depending on their size
1 Tbsp. coarse sugar
Powdered sugar, whipped cream, or crème fraîche (for serving; optional)

Preheat an oven to 375°F. Cook butter in a small saucepan over medium heat, stirring often, until it foams, then browns, 5–8 minutes. Set aside.
Pulse pistachios in a food processor until finely ground. Transfer 4 Tbsp. to a small bowl; set aside.
Scrape reserved browned butter over pistachios in food processor; add egg, brown sugar, flour, salt, and baking powder. Pulse until incorporated, then process, scraping down sides as needed, until mixture looks like wet sand and holds together when squeezed in your hand, about 2 minutes.
Press dough evenly into bottom and about 2" up sides of pan with a straight-sided glass or measuring cup. Chill while you make the filling.
Filling and assembly
Process eggs and brown sugar in clean food processor until eggs are well combined, about 1 minute. Scrape down sides; add sour cream, vanilla bean paste, cardamom, ginger, orange zest, and salt. Sprinkle flour and 2 Tbsp. reserved pistachios over; process until smooth, about 1 minute.
Starting at the edges of the chilled tart shell and working inward, arrange stone fruit in snug concentric circles, standing each wedge up so one tip is raised and rounded skin side is pressed against crust. Carefully pour custard around fruit (fruit should not be completely covered). Sprinkle coarse sugar over.
Bake pie until crust is golden brown and filling is puffed and set in the center (it shouldn’t wobble when gently shaken), 70–75 minutes. Transfer pan to a wire rack and scatter remaining reserved 2 Tbsp. pistachios over. Let cool, then chill, uncovered, until fully set.
Unmold tart. Dust with powdered sugar and/or top with dollops of whipped cream or crème fraîche if desired. Serve chilled or room temperature.