Preheat the oven to 325 degrees.
Grease an 8x8 inch pan (I used a glass pan) with butter.
Put the 4 tbs of butter and 3/4 cup of white chocolate chips in a small bowl. Put that bowl over a pan of boiling water until the chocolate and butter melt into each other. Remove the small bowl from the boiling water.
In a separate bowl, mix the eggs and sugar with an electric mixer until light and creamy( creamy may not be the best word- a mixture of foamy and creamy- this should take about 4 minutes).
Add the melted white chocolate and butter mixture, flour, baking powder and vanilla to the egg mixture and beat with an electric mixer until smooth.
Fold 3/4 cup of the white chocolate chips and 3/4 cups of the dark chocolate chips into the mixture.
Bake for 25 minutes.
Let cool for about 20 minutes and then cut OR eat warm right away :)
Makes about 15- 20 brownies, depending on how small or large you cut them.