Sift together the flour, baking soda and salt.
In the bowl of an electric mixer, cream the butter for 2 -3 minutes or until fluffy and pale yellow.
Scrape down the sides of the bowl and add the sugar. Beat for 1 - 2 minutes or until smooth. Add the egg and vanilla extract and beat on low speed to incorporate.
Gradually add the flour mixture at low speed and beat until just incorporated. Add the chocolate chunk and white chocolate chips and beat or stir to incorporate them into the dough.
Place a piece of parchment paper, wax paper or plastic wrap onto your work surface. Scoop up the dough and form it into 2 logs of about 2 inches in diameter. Roll them up in the paper or wrap and refrigerate them for at least 2 hours or for as long as a week.
To bake, preheat the oven to 350 degrees Fahrenheit and line a baking sheet with parchment paper.
Cut the logs, using a serrated knife into 1/4 to 1/3 inch thick. Place the cookies on the prepared baking sheet about 1-inch apart.
Bake for 10 to 12 minutes. The cookies are done when they are golden brown around the edges. Remove from the oven and place on cooling racks.
Use as many sheet pans as needed until you bake all the cookies.