Preheat oven to 300°F. Coat a baking sheet with nonstick cooking spray.
Melt butter in a small saucepan over medium heat. Swirl the pan until the butter is lightly browned, about 1 minute. Transfer to a medium bowl. Whisk in sugar. Add egg white, flour, cocoa, unsweetened chocolate, vanilla and salt and whisk until smooth.
Drop the batter by heaping teaspoonfuls, about 2 inches apart, onto the prepared baking sheet. Bake until set in the center, 12 to 15 minutes. Immediately transfer the cookies with a spatula to a rack to cool. (If the cookies begin to stick before all are removed, return the pan briefly to the oven.) Dust the cookies with confectioners' sugar if using.