Prepare the pans and oven: Preheat the oven to 350°F (175°C). Grease three 8-inch (20 cm) round cake pans and line the bottoms with parchment paper. Lightly grease the parchment as well.

Combine the dry ingredients: Whisk the all-purpose flour, baking powder, and salt together in a medium bowl. Set aside.

Cream the butter and sugar: In a large bowl, beat the softened butter and granulated sugar on medium-high speed for about 3 to 4 minutes. The mixture should become noticeably lighter in color and fluffy rather than dense or greasy.

Add the eggs and vanilla: Beat in the eggs one at a time, mixing until each is incorporated before adding the next. Scrape down the bowl as needed. Mix in the vanilla extract. If the mixture looks slightly curdled after adding the eggs, continue with the recipe; it should smooth out once the dry ingredients are incorporated.

Finish the base batter: Whisk the whole milk and sour cream together. With the mixer on low, add the flour mixture in three additions, alternating with the milk mixture in two additions. Begin and end with the flour. Mix only until the last streaks of flour disappear. The batter should be thick, smooth, and spoonable.

Divide the batter: Divide the batter as evenly as possible among three medium bowls. A kitchen scale is helpful for creating layers of similar thickness.

Flavor the three layers: Leave one portion as vanilla. Fold the sifted cocoa powder and 1 tablespoon (15 ml) of the additional whole milk into the second portion until evenly chocolate-colored. Fold the ground freeze-dried strawberries and the remaining 1 tablespoon (15 ml) additional whole milk into the third portion until evenly pink with no pockets of strawberry powder.

Bake the cakes: Spread each batter into a prepared 8-inch pan and smooth the tops. Bake for about 22 to 27 minutes, rotating the pans if your oven browns unevenly. The cakes are done when the tops spring back lightly, the edges begin to pull away from the pans, and a toothpick inserted near the center comes out clean or with a few moist crumbs.

Cool completely: Let the cakes cool in their pans for 10 minutes. Carefully turn them onto wire racks, remove the parchment, and let them cool completely, about 1 hour. Do not frost warm layers.

Make the vanilla buttercream: Beat the softened butter for about 2 minutes until creamy. Gradually add the powdered sugar on low speed. Add the vanilla, salt, and ¼ cup (60 ml) heavy cream, then beat on medium-high for 2 to 3 minutes until fluffy. If the frosting is too stiff to spread cleanly, beat in additional cream 1 tablespoon (15 ml) at a time, using no more than the additional 2 tablespoons (30 ml).

Level and stack the cake: If necessary, trim pronounced domes from the cooled cakes with a serrated knife. Place the chocolate layer on a serving plate or cake board and spread about ¾ cup of buttercream evenly over it. Add the vanilla layer, another ¾ cup buttercream, and then the strawberry layer.

Apply a crumb coat: Spread a thin layer of buttercream over the top and sides to trap loose crumbs. Refrigerate the cake for 20 minutes, until the coating feels firm.

Finish the frosting: Cover the chilled cake with the remaining buttercream, smoothing the top and sides with an offset spatula. For a softer homemade finish, create gentle swirls instead of perfectly smooth sides.

Garnish and serve: If desired, decorate with the crushed freeze-dried strawberries and chocolate shavings. For cleaner slices, let the finished cake stand for about 10 minutes after its final chilling before cutting.