Heat oven to 325°F. Coat 8 x 8 x 2-inch baking pan with cooking spray.
Mix butter and 1/2 cup chips in small metal bowl over simmering water; stir to melt. Cool slightly.
Mix white chocolate, shortening in second bowl over simmering water; stir to melt. Cool slightly.
Beat 1 egg, 1/2 cup sugar, vanilla and 1/8 teaspoon salt in bowl until foamy, 30 seconds. Stir in melted dark chocolate mixture and 1/2 cup flour. In second bowl, beat remaining egg, sugar, salt until foamy, 30 seconds. Stir in melted white chocolate mixture and remaining 1/2 cup flour. Add remaining 1/2 cup chips to dark chocolate mixture.
Drop heaping tablespoons batter into pan; alternate dark, white. Marbleize with knife.
Bake in 325°F oven 35 to 40 minutes, until pick tests clean. Cool in pan on rack. Cut into 16 squares.