Preheat oven to 325ºF. Line 2 rimmed baking sheets with parchment. In a medium bowl, whisk together flour, cocoa, baking soda and salt.
Melt chocolate and butter in a double boiler set over simmering water, stirring occasionally. Remove from heat and let cool slightly. Combine chocolate mixture, brown sugar, egg and vanilla in a large bowl and beat until mixture is well combined. Gradually stir flour mixture into chocolate mixture. Add chips.
Roll dough into 16 1 1/2-inch balls, then roll each in sugar. Transfer dough balls to baking sheets, and bake until cookies are puffed and lightly browned, 12 to 15 minutes. Transfer cookies to wire rack and let cool. Repeat with remaining dough.
Arrange 12 cookies bottom side up and top each with a small scoop of ice cream. Top with a second cookie, bottom side down, pressing together slightly. Wrap each in plastic and freeze until firm, about 1 hour.