Prepare the baking dish. Preheat an oven to 350°F (175°C) with a rack set in the center, then grease a 9x13 baking dish with butter or nonstick baking spray.
Mix the dry ingredients. In a large bowl, whisk together 1½ cups (210g) cake flour, ½ cup (65g) ground pistachios, 1 tsp baking powder, and ½ tsp kosher salt. Set aside.
Beat the wet ingredients. Place ⅔ cup (133g) sugar and 6 egg yolks in the bowl of a stand mixer fitted with paddle attachment. Beat on medium to medium-high speed for about 5 minutes. Add 2 tsp almond extract, 1 tsp vanilla extract, and ½ cup (118ml) heavy cream, reserving the rest. Mix on low speed until just combined.
Fold in dry ingredients. Carefully add the flour to the wet ingredients, then gently fold to combine. Transfer to a large mixing bowl, then clean out the stand mixer bowl.
Whip egg whites. Place 6 large egg whites in the stand mixer bowl, then add ¾ tsp cream of tartar. Beat on high speed until stiff peaks form, about 3 minutes.
Fold egg whites into wet ingredients. In three batches, gently fold the egg whites into the cake batter until fully incorporated.
Bake the cake. Pour the cake batter to the prepared baking dish, then use an offset spatula to smooth into an even layer. Transfer to the preheated oven and bake for 20-25, or until a cake tester inserted into the center of the cake comes out clean.
Mix three milks. While the cake is baking, combine remaining ½ cup (118ml) heavy cream, 1 (14oz) can sweetened condensed milk, and 1 (12oz) can evaporated milk in a bowl, then whisk well. Add ⅓ cup pistachio cream, then whisk into the milk mixture.
Drench the cake in tres leches. As soon as the cake comes out of the oven, use a wooden skewer (or fork) to poke holes all over the top of the cake. Pour the milk mixture evenly over the top. Cool to room temperature, about 30 minutes.
Chill overnight. Cover the cake with plastic wrap, then refrigerate for at least 4 hours or up to overnight.
Garnish, then serve. When ready to serve, combine 1½ cup (355ml) heavy cream and 2 Tbsp powdered sugar in the bowl of a stand mixer fitted with whisk attachment. Whip until medium or stiff peaks form (depending on which you prefer). Spread into an even layer on top of the cake, then garnish with chopped pistachios. Enjoy!