Position 2 oven racks in the center of the oven and preheat to 325 degrees F. Line 2 baking sheets with parchment. Combine the granulated sugar and 1 teaspoon of the cinnamon in a small bowl and set aside.
Whisk together the flour, baking soda, 1/4 teaspoon salt and the remaining 1/8 teaspoon cinnamon in a medium bowl. Whisk together the brown sugar, melted butter and corn syrup in a large bowl until smooth. Add the vanilla and egg and whisk until combined. Add the flour mixture and stir with a rubber spatula until just incorporated. The dough will be quite loose; refrigerate for 15 minutes to let it firm up a little.
Scoop out 12 mounds of dough, about 2 scant tablespoons each, and place them at least 2 inches apart on the prepared baking sheets. (The cookies will spread a lot during baking.) Lightly flour your hands and press the dough to about 1/4 inch thick. Sprinkle each cookie with some cinnamon sugar, using all of it.
Bake, switching the sheets halfway through, until the cookies are lightly browned at the edges, 10 to 12 minutes. Let the cookies rest on the sheets for 5 minutes, then carefully transfer to a rack to cool completely, about 20 minutes.
To assemble: Turn 6 cookies upside down on a cutting board. Scoop about 1/3 cup of the ice cream onto each cookie, and spread with a spoon or butter knife to the edge. Top each with a second cookie, and press down gently to adhere. Serve the ice cream sandwiches right away, or put them in the freezer to harden for about 1 hour, then wrap and freeze for up to 2 weeks.
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