Butter and flour two 9-inch round cake pans. Line bottoms with waxed paper cut to fit; butter paper and dust with flour.
In a small bowl, mix 1 1/2 cups cake flour, 1/4 cup sugar, baking powder, 1/2 cup chopped pistachios (wrap remaining airtight), poppy seeds, lemon peel, orange peel, and cardamom.
In a glass measure or small microwave-safe bowl, melt 2 tablespoons butter in a microwave oven on full power (100%), 1/2 to 1 minute. Add milk and vanilla.
In a deep bowl, with a mixer on high speed, beat eggs with remaining 1 cup sugar until thick enough to hold mounds briefly when you lift the beater, 4 to 5 minutes. Add flour mixture and milk mixture. Stir or mix gently until well blended. Scrape batter equally into prepared pans.
Bake cake layers on center rack in a 325° regular or convection oven until edges are browned and begin to pull from pan sides and centers spring back when lightly pressed, 20 to 25 minutes.
Cool layers in pans on a rack for about 10 minutes. Invert cakes from pans onto rack and carefully pull off and discard waxed paper.
When layers are cool to touch, place one, bottom side up, on a flat plate (10 to 12 in. wide). Mound about 2 cups of the Cream Frosting on cake; with a long, flexible metal spatula, spread frosting level out to cake rim. Place remaining cake layer, bottom side down, on frosting. Scrape remaining frosting on top of cake and, with the spatula, push enough over the sides to frost thickly, then swirl evenly over top of cake. Cover (a large bowl inverted over the cake works best) and chill at least 2 hours or up to 1 day.
Uncover cake and sprinkle with remaining 1/4 cup pistachios. On each dessert plate, spoon 3 to 4 tablespoons Sesame Custard Sauce. Cut cake into wedges and set in sauce on plates.
Cream Frosting. In a chilled large bowl, with a mixer on high speed, beat 1 1/2 cups whipping cream until it holds soft, distinct peaks. Add 1/2 cup sour cream, 1/4 cup sugar, and 1/2 teaspoon each almond extract and vanilla. Beat on high speed until mixture is thick enough to hold soft, distinct peaks. Use to fill and frost Pistachio Cream Cake (preceding).