Preheat oven to 180°C (350°F) standard or 160°C (320°F) fan-forced. Line an 8-inch round cake pan.
Pulse pistachios until finely chopped in a food processor.
Mix pistachio crumbs, caster sugar, flour, lemon zest, baking powder, and salt in a large bowl.
Whisk oil, vanilla, eggs, milk, and yogurt in another bowl until combined.
Gently fold wet ingredients into dry ingredients until just mixed.
Spoon batter into the prepared pan and bake for 30-35 minutes until a skewer comes out clean. Cool on a wire rack.