In a large bowl, beat together butter and sugar until light and fluffy, about four minutes.
Add salt and vanilla and beat one minute. Add egg and beat until combined.
Add half the flour and beat to combined. Scrape down sides of bowl with a spatula, add remaining flour, and beat until just incorporated. Use the spatula to fold in the dark and white chocolate chunks.
Wrap dough in plastic wrap and let chill in refrigerator for one hour.
Preheat oven to 375°F. Line two baking sheets with parchment paper.
Drop dough onto prepared baking sheets, using about one heaping tablespoon per cookie. Bake until cookies are brown at the edges and dry on top, about 14 minutes.