Preheat your oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper, leaving an overhang on two sides.
Melt the butter and 1/2 cup of chocolate chips together in a large microwave-safe bowl, stirring every 30 seconds, until smooth. Whisk in the cocoa powder, then both sugars, and let the mixture cool for 5 minutes.
Whisk in the yogurt and vanilla until smooth. Add the flour, baking soda and salt and fold gently just until no dry streaks remain.
Spread the batter evenly into the pan and bake for 24 to 28 minutes, until a toothpick comes out with moist crumbs. Let the brownies cool completely in the pan, about 2 hours.
For the ganache, heat the heavy cream until steaming but not boiling, then pour it over 1 cup of chocolate chips in a bowl. Let it sit for 5 minutes, whisk until silky, then let it cool for 10 minutes so it thickens slightly.
Pour the ganache over the cooled brownies and spread it into a smooth, even layer. Immediately scatter the rainbow chip sprinkles over the top so they stick.
Refrigerate for 30 to 45 minutes, until the ganache is set. Cut into 16 squares and store in an airtight container for up to 4 days.