Preheat oven to 350°F (180°C). Spray 3 tall-sided 9-inch round cake pans with baking spray with flour. Line bottom of pans with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla.
In a medium bowl, whisk together cake flour, ¼ cup (31.5 grams) all-purpose flour, baking powder, and salt. With mixer on low speed, gradually add flour mixture to butter mixture alternately with milk, beginning and ending with flour mixture, beating just until combined after each addition. Divide batter among 3 bowls, weighing about 410 grams each.
Add ½ cup (160 grams) strawberry preserves and remaining ¼ cup (31.5 grams) all-purpose flour to first bowl, folding until combined.
In a small bowl, combine cocoa, ¼ cup (60 grams) boiling water, and baking soda. Fold cocoa mixture into second bowl.
Add half of Pistachio Paste (122 grams) to third bowl, folding until combined. Spoon batters into prepared pans, smoothing tops with an offset spatula.
Bake until a wooden pick inserted in center comes out clean, 20 to 25 minutes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on wire racks.
Place strawberry cake layer on a cake plate. Pipe a border of buttercream around edge of strawberry layer. Spread remaining ½ cup (160 grams) strawberry preserves inside buttercream border. Place chocolate cake layer on top of preserves, and pipe a border of buttercream around edge.
In a small bowl, stir together ½ cup (120 grams) Vanilla Buttercream and remaining Pistachio Paste; spread ½ cup of mixture inside buttercream border on chocolate layer. Top with pistachio cake layer. Spread remaining Vanilla Buttercream on top and lightly on sides of cake. Garnish with pistachios and freeze-dried strawberries, if desired.
Recipe by Bake from Scratch at https://staging.bakefromscratch.com/spumoni-cake/