1. Position the oven racks in the lower and upper thirds of the oven and heat the oven to 350 degrees. Line two baking sheets with Silpats or parchment paper.
2. Sift the flour and baking soda into a medium bowl. Stir in the salt.
3. Put the chips in a fine-mesh basket strainer and shake to remove any chocolate "dust" (small fragments).
4. In the bowl of a stand mixer fitted with the paddle attachment, beat half the butter on medium speed until fairly smooth. Add both sugars and the remaining butter, and beat until well combined, then beat for a few minutes, until the mixture is light and creamy. Scrape down the sides of the bowl. Add the eggs one at a time, beating until the first one is incorporated before adding the next and scraping the bowl as necessary. Add the dry ingredients and mix on low speed to combine. Mix in the chocolate.
5. Remove the bowl from the mixer and fold the dough with a spatula to be sure that the chocolate is evenly incorporated. The dough or shaped cookies can be refrigerated, well wrapped, for up to 5 days or frozen for up to 2 weeks. Freeze shaped cookies on the baking sheets until firm, then transfer to freezer containers. (Defrost frozen cookies overnight in the refrigerator before baking.)
6. Using about 2 level tablespoons per cookie, shape the dough into balls. Arrange 8 cookies on each pan, leaving about 2 inches between them, because the dough will spread. Bake for 12 minutes, or until the tops are no longer shiny, switching the position and rotating the pans halfway through the baking.
7. Cool the cookies on the pans on cooling racks for about 2 minutes to firm up a bit, then transfer to the racks to cool completely. Repeat to bake the remaining cookies. (The cookies can be stored in an airtight container for up to 2 days.)