Preheat oven to 350˚F and grease and flour 2 8-inch baking pans. 

Grind pistachios in a food processor or food mill until they become a fine meal similar to almond flour.

In a mixing bowl, combine ground pistachios, flour, baking powder, matcha, and salt. Whisk until evenly distributed. Set aside.

In a large bowl with an electric mixer, beat the vegan butter, vegetable shortening and sugar until light and fluffy, about 2 minutes.

Add eggs, one at a time, beating until each egg is incorporated.

Mix in the milk, yogurt, vanilla extract and almond extract until combined.

About 1/2 cup at a time, add the flour mixture to the wet ingredients, beating until combined. Continue until everything is mixed together, scraping the sides as needed.

Pour batter into prepared pans and bake for 35 - 40 minutes, or until an inserted toothpick comes out clean.

Remove from the oven and allow cakes to cool to room temperature before frosting.

Add white chocolate chips to a small mixing bowl. Microwave for 2 30-second intervals, stirring between to help the chocolate melt. If needed, continue to heat for 10 second intervals, until the chocolate is melted after stirring.

In a large bowl with an electric mixer, beat the butter or shortening with salt, vanilla extract and almond milk. Add melted chocolate and about 1 cup of powdered sugar. Mix until combined.

Then, add about 1 cup of powdered sugar at a time until you reach your desired consistency.

Frost cake as desired.