Preheat the oven to 325°F. Grease and flour a 8 x 8 inch baking pan.
In a medium bowl, gently whisk together the flour, baking powder and salt.
In a small saucepan, slowly melt butter and one third of the white chocolate chips over low heat, whisking constantly. Remove from heat as soon as butter and chocolate chips are melted.
In a large bowl use an electric mixer to beat together eggs, sugar, and vanilla until smooth and light. Add butter and white chocolate mixture, beating until well combined.
Slowly add the dry ingredients to the wet mixture.
Fold in remaining white chocolate chips.
Pour batter into prepared baking pan and bake 40-45 minutes.
Remove from oven and allow to cool completely before cutting.
Optional Once cooled completely, dust with powdered sugar before serving.