Start by finely grinding the pistachios in a food processor until you get a soft meal. Mix your dry ingredients (flour, baking powder, and salt) in one bowl, and the wet ingredients (milk, olive oil, vanilla, almond extract, and vinegar) in another. Gently combine both mixtures, taking care not to overmix.
Pour the batter evenly into greased and lined 8-inch cake pans. Bake at 350°F (175°C) for 35–40 minutes or until a toothpick inserted in the center comes out clean. Let the cakes cool completely on a cooling rack to prevent the buttercream from melting.
Whip the salted butter until creamy and light. Gradually add powdered sugar, then fold in blackberry preserves and a pinch of dried thyme for a sophisticated, slightly herbal flavor. Chill the buttercream slightly for easier spreading.
Level the tops of your cakes with a serrated knife. Spread a generous layer of blackberry preserves on one cake layer, then pipe or spread a thick layer of the buttercream. Place the second cake layer on top and frost the sides and top evenly.
Decorate with fresh blackberries and thyme sprigs just before serving. This adds freshness and a vibrant, beautiful look. Run a warm knife under water and wipe it dry before slicing for clean edges.