Line a 13- x 9-inch baking pan with foil; grease foil, and set aside. Beat butter and brown sugar in a large bowl at medium speed with an electric mixer until fluffy. Beat in 2 eggs and vanilla.
Combine flour, baking powder, and salt in a separate bowl; stir into butter mixture. Spoon 1 1/2 cups of batter into a medium bowl; add the remaining 2 eggs, sugar, and melted white chocolate, stirring until well blended. To the batter remaining in the large bowl, add melted dark chocolate and unsweetened chocolate.
Drop alternating teaspoonfuls of the light and dark batters into prepared pan. Bake at 350° for 30 to 35 minutes or until a toothpick inserted in center comes out clean. Let cool completely on a wire rack. Lift from pan by the foil; cut into squares.
*Use good-quality white chocolate; white candy coating will not work in this recipe.