Preheat oven to 350°F (175°C). Grease and flour two 6- or 7-inch round cake pans.

In a medium bowl, combine milk and apple cider vinegar, let sit for 5 minutes.

Pulse ground pistachios with sugar in a food processor until finely ground.

In a large mixing bowl, whisk together ground pistachios, flour, baking powder, and salt.

Whisk together buttermilk, olive oil, vanilla extract, and almond extract in another bowl.

Fold dry ingredients into wet mixture, being careful not to overmix.

Pour cake batter evenly into prepared pans and bake for 25-30 minutes.

Cool on a wire rack for about 10 minutes before removing from pans to cool completely.

Beat butter and blackberry preserves, add powdered sugar, vanilla extract, and optional thyme to make frosting.

Level one cake layer, spread buttercream and blackberry preserves, top with second layer, then frost entire cake.

Garnish with fresh blackberries and chopped pistachios before serving.