Preheat your oven to 350°F (175°C). Grease two 6- or 7-inch cake pans with olive oil, then dust with flour. Cut circles of parchment paper to fit the bottom of the pans.

In a small bowl, mix your choice of milk with apple cider vinegar or lemon juice. Let it sit for about 5 minutes until it curdles slightly, creating buttermilk.

Blend the ground pistachios with granulated sugar in a food processor. In a large bowl, whisk together flour, baking powder, and salt. Incorporate the pistachio-sugar blend into the dry mixture.

In a separate bowl, whisk together curdled buttermilk, olive oil, vanilla extract, and almond extract. Gently fold this into the dry ingredients to create the batter.

Fold together the wet and dry ingredients gently until just combined. Be careful not to overmix.

Divide the batter evenly between the prepared pans, smoothing the tops. Bake for 25 to 30 minutes until a toothpick comes out clean.

Allow the cake layers to cool in the pans for about 10 minutes. Then, remove them and transfer to a wire rack. Wrap cooled layers in plastic wrap and refrigerate overnight.

Beat softened butter in a bowl until creamy. Gradually add blackberry preserves and powdered sugar until fluffy. Optionally mix in dried thyme.

Once the layers are chilled, level the top of the first layer, spread frosting, add blackberry preserves, then top with the second layer and frost the entire cake.

Garnish with fresh blackberries and chopped pistachios before serving.