Preheat the oven to 350 F. Line the bottom of a buttered 8 x 8-inch baking pan with parchment paper, then butter the paper. Place pistachios and lemon zest into a food processor bowl; pulse until finely ground (but not pistachio butter). Transfer mixture into a bowl. Add flour, baking powder and baking soda. Whisk to combine; set aside. Whisk together sour cream, vanilla and milk in a small bowl; set aside.
In the bowl of a stand mixer fitted with paddle attachment, cream butter, sugar and salt on medium speed until light and fluffy, about 3 minutes. Add eggs, one at a time, until fully incorporated. With mixer on low, alternate adding the dry ingredients (in 3 additions) and the wet ingredients (in 2 additions), starting and ending with the dry ingredients.
Pour the batter into the prepared pan; smooth the top. Bake 35 to 40 minutes, or until a toothpick inserted in the center comes out clean. Cool 10 minutes. Carefully remove cake from pan, peel off the parchment paper, then invert onto a wire rack to cool completely.
Prepare the frosting: Combine all frosting ingredients in a medium bowl. Mix just until smooth, being careful not to overmix or curdle the frosting. Frost the cake, then sprinkle on extra chopped pistachios. Serve or refrigerate until serving. Makes 8 servings.