Preheat oven to 350 degrees F. Line an 8x8 metal square baking pan with foil, extending the sides of the foil over the edges of the pan. Spray the foil liberally with cooking spray; set aside.
In a large microwave-safe bowl, add in the cubed butter and chopped white chocolate bars. Microwave on HIGH power for 20 seconds. Stir, then microwave for another 20 seconds, stirring in between interval bursts of 20 seconds until mixture is smooth and melted cohesively. It's important to melt the white chocolate very slowly in small bursts because it is prone to seizing very easily. Once mixture has melted and is smooth, let set for 5 minutes to cool off some.
Add in the sugars, eggs, and vanilla and stir with a rubber spatula until combined. Lastly, stir in the salt and flour until a soft batter comes together. Gently fold in the rainbow sprinkles.
Spread the batter evenly into the baking pan and smooth out the top. Bake for approximately 25-35 minutes or until the top is light golden brown and a toothpick inserted near the center comes out clean. Cool completely before cutting into bars.