Preheat oven to 350 degrees. Line a 9 x 9 inch baking pan with parchment paper; set aside.
In a microwave safe bowl, melt ½ cup of chocolate chips and ½ cup of butter at 50% power until melted; about 90 seconds. Stir and set aside.
In a large bowl, use a handheld mixer to beat together the sugar and eggs until well combined and frothy. Mix in the cooled chocolate, flour, sour cream, and vanilla until combined. Fold in the remaining ½ cup of chocolate chips.
Pour the brownie mixture into the prepared baking pan. Bake for about 30 minutes or until the brownies start to pull away from the edge of the pan. Remove from oven and cool on rack before adding the frosting.
To make the frosting, microwave the butter and cocoa powder until the butter is melted. Whisk together and add in the vanilla and milk until well combined. Add in the powdered sugar and whisk until you get a thick frosting. Spread the frosting over the cooled brownies and cut into to squares.
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Notes
This is a great recipe to use leftover sour cream. I prefer to use the full fat sour cream for baking.
The brownie batter will be lighter than normal since you don't add any cocoa powder to the batter.
Be sure the brownies are cooled before adding the frosting otherwise you risk the frosting moving around and no hardening on top.
Store these brownies in an airtight container in the refrigerator for up to a week.