Preheat oven to 350°F / 175°C. Line the bottom and the sides of a 9" (23cm) springform pan with parchment paper. Set aside.
Place pistachios in a food processor and pulse into fine crumbs. Don't grind too long. Otherwise, it turns into a paste. Transfer to a bowl and add flour, baking powder, and salt. Stir to combine. Set aside.
In a large mixing bowl with a stand or handheld mixer fitted with a whisk or paddle attachment, beat butter and sugar until creamy for about 2-3 minutes. Add 1 egg at the time and mix until incorporated. Add sour cream and vanilla* and stir to combine. Alternately add dry ingredients and milk, beginning and ending with dry ingredients. Stir just until combined.
Transfer to the prepared baking pan and bake for about 25-28 minutes or until a toothpick in the center comes out clean. Let cool in pan for 20 minutes. Then transfer to a wire rack to let cool completely.
Orange pistachio syrup (OPTIONAL): In a medium saucepan over medium-low heat, cook pistachios, sugar, orange juice, and orange zest until sugar is completely dissolved and syrup coats the back of a spoon, about 3-4 minutes.
Pour syrup over cooled cake slices just before serving. Store leftover cake in an airtight container at room temperature up to 2 days. Reheat leftover syrup to liquefy again, if necessary.