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

Combine milk with apple cider vinegar in a small bowl and let it sit for 5-10 minutes to thicken slightly.

Finely grind pistachios and granulated sugar in a food processor until it resembles sand.

In a medium bowl, whisk together the pistachio-sugar mixture, all-purpose flour, baking powder, and salt until well mixed.

Blend the prepared buttermilk, olive oil, and vanilla extract in a large bowl until smooth.

Gently fold the dry ingredient mixture into the wet mixture, stirring until just combined.

Divide the batter between the prepared cake pans and bake for 25-30 minutes or until a toothpick comes out clean.

Remove cakes from the oven and let them cool in the pans for about 10 minutes before transferring to wire racks to cool completely.

Beat room temperature butter and blackberry preserves until fluffy. Gradually add powdered sugar and dried thyme until desired consistency.

Assemble the cake by frosting one layer, adding the second layer, and frosting the top and sides. Decorate with fresh blackberries and chopped pistachios.