In a stand mixer, whisk eggs, sugar and vanilla on a high speed until pale, soft and fluffy.
In a separate bowl, sift together flour, baking powder and matcha. Add this to the eggs a third at a time while beating the egg mixture on a slow speed.
Meanwhile, whisk together melted butter, milk and oil. Scoop out half a cup of the egg mixture and stir it into the butter, then pour all back in to the batter and fold through. Cover with plastic wrap and chill for two hours.
Preheat oven to 160ºC. Prepare madeleine mould by spraying lightly with oil or butter and dusting with flour. Using a teaspoon, scoop batter into moulds until about three quarters full.
Bake for 10 minutes before removing tray and tapping on a flat surface. Continue baking for a further five minutes until madeleines are slightly golden around the edges. Remove from moulds and place on a wire wrack to cool.
Place white chocolate in a bowl and microwave for a minute and a half, stirring at each 30 second interval until chocolate is smooth and silky.
Dip half of each cooled madeleine in chocolate and sprinkle with pistachios.