Preheat the oven to 375°F. Lightly grease (or line with parchment) three baking sheets. If you don't have three baking sheets, that's OK; you'll bake the cookies in batches. , To make the dough: In a large bowl, combine the sugars, butter, shortening, salt, baking soda, vanilla and almond extracts, and vinegar, beating until smooth and creamy. , Add the egg, beating again until smooth. Scrape the bottom and sides of the bowl with a spatula to make sure everything is thoroughly combined. , Mix in the flour, stirring just until combined. , Divide the dough in half; if you have a scale, each half will weigh about 390g. , Mix the cocoa, milk, and white chocolate chips into one half of the dough. , Mix the semisweet chocolate chips into the other half of the dough. , To shape the cookies: Use a teaspoon cookie scoop to portion the chocolate chip cookie dough onto one of the baking sheets; the balls of dough can be close together. Repeat with the white chocolate chip dough. , Cover the baking sheet and refrigerate the dough balls for 30 minutes. , Working with one chocolate chip dough ball and one white chocolate chip dough ball at a time, gently press the two together and roll them into a single ball, being careful not to completely blend them. , Place the marbled dough ball onto one of the prepared baking sheets. Repeat with the remaining dough balls, leaving 2" clearance among the cookies. , To bake the cookies: Bake the cookies for 9 to 11 minutes, until their edges are set and the middles are still slightly soft. , Remove the cookies from the oven and cool them on the pan until they're set enough to move without breaking. , Storage information: Store cookies, well wrapped, at room temperature for several days; freeze for longer storage.