Preheat your oven to 350°F (175°C).
Grease and line an 8x8-inch baking dish with parchment paper.
In a large bowl, whisk together the flour, granulated sugar, ground pistachios, baking powder, baking soda, and salt.
In another bowl, mix the plant-based milk and apple cider vinegar to create a dairy-free buttermilk. Let it sit for a few minutes until it curdles slightly.
Add the vegetable oil, dairy-free yogurt, and vanilla extract to the buttermilk mixture and mix until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined. Do not overmix.
Pour the batter into the prepared baking dish and spread it evenly.
Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the sponge to cool in the dish for 10 minutes.