Preheat the oven to 350F and grind the pistachios into a powder. To do this, add them to a food processor and pulse them until they are ground into small pieces, but not too long, or they can turn into a paste.
First, add the oat milk and lemon juice to a bowl and mix together. Let sit for 1-2 minutes to curdle to make the vegan buttermilk.
Then, add in the sugar, olive oil, and vanilla. Whisk the wet ingredients together.
Next, add in the dry ingredients, starting with the all-purpose flour then layering the ground pistachios, baking powder, salt, and baking soda on top.
Mix into a thick batter. I recommend starting with a whisk and then switching to a spatula so the batter does not get over-mixed.