For the cake:
Vegetable oil, for cake pan
1 1/2 cups shelled unsalted pistachios (8 ounces)
3/4 cup sugar, divided
6 large eggs, at room temperature
1 teaspoon vanilla extract
1/2 teaspoon kosher salt, plus more for egg whites
1/4 teaspoon ground cardamom
For meringue topping:
1 1/3 cups freeze-dried strawberries (1.2-ounce package)
5 egg whites, at room temperature
1/2 teaspoon white vinegar
1 cup almond flour (4 ounces)
1 cup superfine sugar
1 tablespoon potato starch
Make the cake:
Preheat oven to 325°F. Lightly brush a 9-inch springform pan with oil and line bottom with a round of parchment paper. Brush parchment with oil and set pan aside.
In a food processor, pulse pistachios with 1/4 cup sugar until finely ground (avoid overgrinding); set aside.
In two large bowls, separate the 6 eggs into yolks and whites, reserving the sixth egg white for another use. Add 1/4 cup sugar, vanilla, salt, and cardamom to bowl with egg yolks and beat using an electric mixer until thick and pale yellow, about 2 minutes.
Set egg yolk mixture aside and thoroughly clean and dry the beaters.
Add a pinch of salt to the bowl with the egg whites and beat using an electric mixer until soft peaks form. Gradually beat in remaining 1/4 cup sugar, and continue beating until stiff peaks form.
Add half of the whipped egg whites and all of the ground pistachios to the egg yolk mixture and fold until combined. Add the remaining egg whites and fold until batter is just combined.
Pour batter into prepared pan and smooth top with a rubber spatula. Bake until beginning to brown and just barely set, 20–25 minutes.
Meanwhile, make the meringue topping:
In a food processor, process the strawberries into a fine powder. Set aside 1 Tbsp. of the powder for decorating the cake, and pour the remaining powder into a medium bowl.
Whisk in the almond flour and the potato starch.In a large bowl using an electric mixer, beat 5 egg whites and vinegar until soft peaks form, then gradually beat in the sugar and continue to whip until meringue is stiff and glossy and all the sugar has dissolved, 7–8 minutes.
Gently fold almond mixture into meringue until just combined.
Remove cake from oven. Using an offset spatula or table knife, spread meringue mixture evenly over hot cake, starting from the outside and working your way into the center.
Return cake to oven and bake until meringue is lightly browned and crisp, 25–30 minutes. Transfer pan to a wire rack to cool, and immediately run a knife around the edge of the cake to loosen it from the pan. Release and remove the side of the springform pan. Let cake cool at least 30 minutes before decorating.