3/4 cup plus 2 tablespoons all-purpose flour
1/4 cup natural unsweetened cocoa powder
1/2 teaspoon baking soda
1/2 teaspoon kosher salt
6 tablespoons (3/4 stick) unsalted butter, room temperature
1/2 cup sugar
1 tablespoon light corn syrup
1 large egg yolk
1 teaspoon pure vanilla extract
1 tablespoon sour cream
1 pint ice cream (any flavor)
Whisk flour, cocoa powder, baking soda, and salt in a medium bowl. Using an electric mixer, beat butter, sugar, and corn syrup in another medium bowl until light and fluffy, about 3 minutes. Add egg yolk and vanilla; beat until combined.
Reduce mixer speed to low, add dry ingredients, and mix until just combined. Mix in sour cream. Form dough into a 3/4-inch-thick square, wrap tightly in plastic, and chill until firm, 2–3 hours.
Preheat oven to 350°. Roll out dough between 2 sheets of parchment to about 1/8-inch thickness. Transfer dough (still between parchment) to a large baking sheet and chill until firm, at least 30 minutes. Remove top sheet of parchment (it will come away easily if dough is well chilled) and trim to a 14×10-inch rectangle. Bake cookie until dry and just set at edges, 8–10 minutes. Transfer baking sheet to a wire rack; let cookie cool.
Trim cookie to a 12×9-inch rectangle, then cut into twelve 3-inch squares. Scoop ice cream into a medium bowl and mix just until softened, 2–3 minutes. Turn 6 cookies bottom side up. Dividing evenly, scoop ice cream on top and flatten slightly; top with remaining cookies, pressing down gently. Place sandwiches on a parchment-lined baking sheet and freeze until firm, at least 4 hours. Cut sandwiches in half on a diagonal to make triangles. Wrap in parchment, if desired, and freeze until ready to serve.
DO AHEAD: Ice cream sandwiches can be made 1 week ahead. Keep frozen.