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

In a small bowl, combine your chosen milk with apple cider vinegar or lemon juice and let it sit for about 5 minutes.

Pulse the ground pistachios with sugar in a food processor until fine but still retains some texture.

In a mixing bowl, whisk together the ground pistachio mixture, all-purpose flour, baking powder, and salt.

In another bowl, whisk together the buttermilk mixture, olive oil, vanilla extract, and almond extract until combined.

Gently fold the dry ingredients into the wet mixture until just combined.

Divide the batter evenly between the prepared pans, and bake for 25-30 minutes.

Allow the cake layers to cool in their pans for 10 minutes before transferring them to a wire rack.

To make the frosting, beat softened butter until creamy, then gradually add blackberry preserves, powdered sugar and thyme.

Level the top of one cake layer, spread frosting and preserves, then place the second layer on top. Coat the entire cake with remaining buttercream.

Garnish with fresh blackberries and chopped pistachios before serving.