Preheat oven to 375. Place pistachios on a baking sheet. Bake until fragrant and toasted, about 7 minutes. Remove and set aside to cool.
Place cooled pistachios in food processor and grind into a coarse flour. Add whole wheat pastry flour, salt, baking soda, baking powder, and cardamom and pulse to combine.
In standing mixer or large bowl, cream butter with white sugar and brown sugar until light and fluffy, about 3 minutes. Add in eggs, one at a time. Use spatula to get any excess butter on the sides of the bowl to help make sure the eggs are well incorporated into the mixture.
Add in vanilla extract, lemon zest, and yogurt. Mix to combine.
Add in flour. mixture in two increments, mixing after each one to combine.
Pour batter into 8'' cake pan- it will be quite thick.
Place rhubarb gently on top and sprinkle with turbinado sugar.
Bake 25-30 minutes at 375, until a toothpick comes out clean.