Preheat oven to 350°F. Line baking sheets with silicone baking mats or parchment.
Whisk together flour, baking soda, and salt in a medium bowl.
Place chocolate pieces in a fine-mesh strainer and shake to remove any dust that would color the cookie batter.
In the bowl of a stand mixer fitted with the paddle attachment, beat half the butter until smooth. Add the sugars and remaining butter and beat until the mixture is light and creamy.
Add eggs, one at a time, beating in the first completely before adding the second egg.
Add the flour mixture and beat on low to combine. Add the chocolate and pulse the mixer to incorporate.
Scoop the dough into 2-tablespoon-sized balls and place on prepared sheets, leaving 2 inches of space between. You should be able to get eight cookies per baking sheet.
Bake for 12 minutes, rotating the sheets from top to bottom, and front to back, halfway through. The cookies will no longer be shiny on top.
Let cool on baking sheets for 2 minutes before using a spatula to transfer to rack to cool completely.