Adjust oven racks to upper- and lower-middle positions and heat oven to 375 degrees. Line 2 large (18- by 12-inch) baking sheets with parchment paper. Place ½ cup granulated sugar in shallow baking dish or pie plate. Whisk flour, cocoa powder, baking soda, and salt together in medium bowl. Whisk corn syrup, egg white, and vanilla together in small bowl.
In stand mixer fitted with paddle attachment, beat butter, brown sugar, and remaining 1/3 cup granulated sugar at medium-high speed until light and fluffy, about 2 minutes. Reduce speed to medium-low, add corn syrup mixture, and beat until fully incorporated, about 20 seconds, scraping bowl once with rubber spatula. With mixer running at low speed, add flour mixture and chopped chocolate; mix until just incorporated, about 30 seconds, scraping bowl once. Give dough final stir with rubber spatula to ensure that no pockets of flour remain at bottom. Chill dough 30 minutes to firm slightly (do not chill longer than 30 minutes).
Divide dough into 16 equal portions; roll between hands into balls about 11/2 inches in diameter. Working in batches, drop 8 dough balls into baking dish with sugar and toss to coat. Set dough balls on prepared baking sheet, spacing about 2 inches apart; repeat with second batch of 8. Bake, reversing position of the baking sheets halfway through baking (from top to bottom and front to back), until cookies are puffed and cracked and edges have begun to set but centers are still soft (cookies will look raw between cracks and seem underdone), 10 to 11 minutes. Do NOT overbake.
Cool cookies on baking sheet 5 minutes, then use wide metal spatula to transfer cookies to wire rack; cool cookies to room temperature.