Preheat oven to 350 degrees. Butter a cookie sheet. Scoop 1 even tablespoon vanilla cookie dough and 1 even tablespoon chocolate cookie dough (using separate scoops or colors will blend), now take each one and carefully meld together while cupping your hands to round edges. Places cookie on cookie sheet and flatten slightly. Do this with remaining dough, baking 12 cookies at at a time. Bake 9 - 11 minutes in preheated oven. Allow to cool several minutes before moving to a wire cooling rack.
White Chocolate Cookie Dough
In a mixing bowl whisk together flour, baking powder, baking soda and salt, set aside. In the bowl of an electric mixer, whip together butter and sugar until light and fluffy. Stir in egg, then add vanilla and milk. Melt vanilla chips in the microwave on 50% power in 30 second intervals, stirring after each interval until melted and smooth. Add melted white chocolate to cookie dough mixture. Slowly stir in dry ingredients and mix until well incorporated. Mix in chocolate chips.
Chocolate Cookie Dough
In a mixing bowl whisk together flour, cocoa powder, baking powder, baking soda and salt, set aside. In the bowl of an electric mixer, whip together butter and sugar until light and fluffy. Stir in egg, then add vanilla and milk. Melt semi-sweet chocolate chips in the microwave on 50% power in 30 second intervals, stirring after each interval until melted and smooth. Add melted chocolate to cookie dough mixture. Slowly stir in dry ingredients and mix until well incorporated. Mix in vanilla chips.