Move oven rack to middle position, and preheat to 350 degrees F. Lightly spray a rimmed cookie sheet with nonstick cooking spray, and line with parchment paper; set aside.
In a medium bowl add flour, cocoa, and baking soda. In a large bowl whisk together eggs, sugar, and chocolate syrup, and melted butter until well blended.
Fold dry ingredients into egg mixture until well combined and no flour streaks remain. Pour batter into the prepared baking sheet, spread batter evenly using an offset metal spatula. Bake until cookie springs back when touched with a finger, 10-12 minutes. Cool in pan on wire rack for 5 minutes, then run a paring knife around the perimeter of the baking sheet to loosen. Invert cookie onto a work surface or large cutting board; carefully peel off parchment. Cool to room temperature, about 30 minutes.
After the cookie layer is done cooling, measure, score, and cut at the halfway point. The cookie has a tendency to stick after cooling, so use a bench scraper to lift it from the cutting board onto a large piece of plastic wrap. Empty the ice cream onto the cookie, and using your clean or gloved hands, squish the ice cream to distribute evenly. Place the second cookie layer on top of the ice cream and wrap in plastic wrap. Place on a cookie sheet and freeze until the ice cream hardens again about 1-2 hours.
Cut the bars into thirds and then each third into four pieces to make 12 ice cream sandwiches. Serve immediately or wrap each ice cream sandwich in plastic wrap and return to the freezer.