To make the cake:
- Preheat oven to 350°F. Line an 8×8″ pan with parchment paper (with a bit of overhang on sides) and lightly grease. Set aside.
- Place pistachios in the bowl of a food processor and process into crumbs. Remove 1 tablespoon of crumbs for garnish. Pour remaining pistachios into a medium bowl. Add flour, baking powder and baking soda to same bowl and whisk to combine. Set aside.
- In a large bowl, stir together sugar and lime zest. Add butter to bowl and beat for 1-2 minutes or until butter mixture is light and fluffy. Add eggs and vanilla extract and beat until thoroughly combined. Add sour cream and milk and beat again until incorporated. Fold in flour mixture until just combined.
- Pour batter into prepared pan and bake for 27-32 minutes or until cake tester comes out nearly clean. Cool on rack in pan.
To make the frosting:
- Beat cream cheese and butter together in a bowl until smooth. Add lime zest and juice and mix until incorporated. Add powdered sugar and mix until smooth.
- Remove cake from pan. Spread frosting on top of cooled cake. Garnish with reserved pistachio crumbs.