Preheat oven to 350 degrees. Line an 8x8-inch baking dish with parchment paper.
In a small bowl, melt chopped dark chocolate in the microwave in 30-second increments. Stir in between increments until melted.
In a large bowl, beat avocado, sugar, melted chocolate and vanilla together with an electric mixer. Add eggs and beat until combined.
Add cocoa powder, flour and salt to the bowl. Beat until well-combined.
Fold in dark and white chocolate chips.
Add batter to the lined pan, spreading evenly. Bake for 40 to 45 minutes, until set. Make sure you do not over bake or the brownies will come out too dry.
Cool completely before slicing and serving.