Preheat your oven to 350°F (175°C) and prepare two 6- or 7-inch cake pans, greasing with olive oil or butter and dusting with flour.

In a medium bowl, combine your choice of milk with apple cider vinegar or lemon juice to create a homemade buttermilk. Let it sit for about 5 minutes.

In a food processor, pulse the ground pistachios with sugar until finely ground. Transfer to a large bowl, sift in flour, baking powder, and salt. Whisk gently to combine.

In a separate bowl, whisk together the prepared buttermilk, olive oil, vanilla extract, and almond extract until thoroughly blended.

Gently fold the wet ingredients into the dry mixture using a spatula, being careful not to overmix.

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

Let the pans cool on a wire rack for about 10 minutes, then invert the cakes to cool completely.

In a mixing bowl, beat room temperature butter until creamy, then gradually add blackberry preserves and powdered sugar until fluffy. Stir in vanilla extract, a pinch of salt, and thyme if desired.

Level the top of the first cake layer with a serrated knife, spread a layer of frosting on top, add a layer of blackberry preserves, then stack the second layer.

Frost the top and sides of the assembled cake, garnishing with fresh blackberries and chopped pistachios.