Note: If measuring by volume, it's important to measure the flour and cocoa lightly, as follows: stir flour briefly in the container or bag, spoon into the measuring cup until it's heaped above the rim, then level it with a straight-edged knife or spatula. If you dip the measuring cup into the container, you'll have more flour and cocoa and a drier, crumblier, more difficult dough.
Sift the flour, cocoa and baking soda together.
Working with a stand mixer, preferably fitted with a paddle attachment, or with a hand mixer in a large bowl, beat the butter on medium speed until soft and creamy. Add both sugars, the salt and vanilla extract and beat for 2 minutes more.
Turn off the mixer. Pour in the dry ingredients, drape a kitchen towel over the stand mixer to protect yourself and your kitchen from flying flour and pulse the mixer at low speed about 5 times, a second or two each time. Take a peek — if there is still a lot of flour on the surface of the dough, pulse a couple of times more; if not, remove the towel. Continuing at low speed, mix for about 30 seconds more, just until the flour disappears into the dough — for the best texture, work the dough as little as possible once the flour is added, and don't be concerned if the dough looks a little crumbly. Toss in the chocolate pieces and mix only to incorporate.
Turn the dough out onto a work surface, gather it together and divide it in half. Working with one half at a time, shape the dough into logs that are 1 1/2 inches in diameter. Wrap the logs in plastic wrap and refrigerate them for at least 3 hours. (The dough can be refrigerated for up to 3 days or frozen for up to 2 months. If you've frozen the dough, you needn't defrost it before baking — let it warm just enough so that you can slice the log into rounds and bake the cookies 1 minute longer.)
Center a rack in the oven and preheat the oven to 325 °F. Line two baking sheets with parchment or silicone mats.
Using a sharp thin knife, slice the logs into rounds that are 1/2 inch thick. (The rounds are likely to crack as you're cutting them — don't be concerned, just squeeze the bits back onto each cookie.) Arrange the rounds on the baking sheets, leaving about 1 inch between them.
Bake the cookies one sheet at a time for 12 minutes — they won't look done, nor will they be firm, but that's just the way they should be. Transfer the baking sheet to a cooling rack and let the cookies rest until they are only just warm, at which point you can serve them or let them reach room temperature.