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

In a small bowl, combine the milk with apple cider vinegar and let it sit for 5-10 minutes to create homemade buttermilk.

Blend the ground pistachios and granulated sugar in a food processor until fine.

In a medium bowl, whisk together the flour, pistachio-sugar blend, baking powder, and salt.

In a large bowl, whisk the homemade buttermilk, olive oil, and vanilla extract until smooth.

Gently fold the dry ingredients into the wet ingredients until just mixed.

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

Remove the cakes from the oven and let them cool in the pans for 10 minutes before transferring to a wire rack.

Combine softened butter with blackberry preserves, beat until fluffy, then add powdered sugar and dried thyme.

Assemble the cake by spreading frosting on the first layer, placing the second layer on top, and frosting the entire cake.