Heat oven to 350°F. Lightly grease 9 x 9 x 2-inch square baking pan. Mix together the flour, baking powder and salt in bowl.
Beat butter, granulated sugar, brown sugar, cocoa, eggs and vanilla in bowl until fluffy and smooth. Stir in flour mixture until blended. Set aside 1/4 cup each milk chocolate morsels and white baking morsels and 2 tablespoons cherries. Fold remaining morsels and cherries into dough. Spoon onto greased baking pan.
Bake in 350°F oven 20 to 25 minutes or until firm in center. While still hot, cut into 16 squares. Melt reserved 1/4 cup milk chocolate morsels; drizzle over bars. Coarsely chop reserved 2 tablespoons cherries; sprinkle over top. Melt white baking morsels with shortening; drizzle over bars. Cool in pan on wire rack. Store in airtight container.