Preheat your oven to 350°F (175°C). Grease two 6 or 7-inch cake pans with olive oil and dust them lightly with flour. Line the bottoms with parchment paper.

In a small bowl, combine the milk (or non-dairy alternative) with apple cider vinegar or lemon juice and let it sit for about 5 minutes.

In a food processor, blend the ground pistachios and sugar until finely ground but still retaining some texture for about 20–30 seconds.

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

In a large mixing bowl, whisk together the buttermilk, olive oil, and extracts until well blended.

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

Divide the batter evenly between the prepared pans (approximately 425 grams per pan) and bake for 25–30 minutes.

Once baked, let the cakes cool completely in the pans on a wire rack for about 10 minutes before turning them out to cool further.

Beat together the softened butter and blackberry preserves, gradually adding powdered sugar, vanilla extract, and dried thyme until fluffy.

Level the top of one cake layer, frost generously, add a layer of raspberry preserves, and place the second cake layer on top before frosting the entire cake.