Preheat the oven to 325 degrees F. Make sure your oven rack is in the top 1/3 of the oven.
Grease an 8x8 inch pan and line with parchment paper.
Put the butter and 3/4 cups of white chocolate chips in a small microwave safe bowl. Microwave in 15 second increments until melted.
In a separate bowl, mix the eggs and sugar with a a hand-held electric mixer until light and a bit foamy. This should take 2 minutes.
Add the melted white chocolate mixture, flour, baking powder and vanilla to the egg mixture and beat with an electric mixer until just mixed.
Fold in 3/4 cups of the white chocolate chips and 3/4 cups of the dark chocolate chips into the mixture. Pour into the greased and lined pan, and push down on the batter with a rubber spatula to evenly spread it in the pan.
Bake for 20-25 minutes. Start checking it at the 20 minute mark. You'll know they are done when the edges start to get a little bit golden and the middle looks set.
Let the brownies cool for 20 minutes prior to cutting. (If you can wait that long). These also taste delicious warm.