Preheat the oven to 350°F. Line baking sheets with parchment paper.
In a mixer, cream together butter and sugars. Mix in egg, egg white and vanilla and mix until smooth.
In a medium bowl, combine cocoa powder, baking soda, salt and flour. Stir to combine.
Working in batches, mix dry ingredients into the butter mixture. Stir until smooth. Fold in 2/3 cup white chocolate chips, 1/4 cup semi-sweet chocolate chips and 1 cup macadamia nuts.
Drop 1 1/2 tablespoon-sized balls onto prepared cookie sheets. Bake for 7 minutes. Cool for 2 minutes before transferring to wire cooling racks to cool completely.
In a small bowl, combine the remaining 1 cup white chocolate chips and 1/2 tablespoon oil. Stir. Microwave for 30 seconds and stir until smooth. If needed, microwave in 10-second increments, stirring in between, until all the chips are melted and smooth. Dip cooled cookies into melted chocolate and place on parchment paper to set.