Sift flour, cocoa, and baking soda into medium bowl.
Using electric mixer, beat butter in large bowl until smooth but not fluffy.
Add both sugars, vanilla, and sea salt; beat until fluffy, about 2 minutes. Add flour mixture; beat just until blended (mixture may be crumbly). Add chopped chocolate; mix just to distribute (if dough doesn't come together, knead lightly in bowl to form ball).
Divide dough in half. Place each half on sheet of plastic wrap. Form each into 1 1/2-inch-diameter log. Wrap each in plastic; chill until firm, about 3 hours. This can be made up to 3 days ahead.
Preheat oven to 325°F.
Line 2 baking sheets with parchment paper.
Using thin sharp knife, cut logs crosswise into 1/2-inch-thick rounds. Space 1 inch apart on prepared sheets.
Bake 1 sheet at a time until cookies appear dry (cookies will not be firm or golden at edges), 11 to 12 minutes.