Preheat the oven to 375 degrees F (190 degrees C) and line an 18x13x1-inch sheet pan with parchment paper.
In an electric mixer fitted with the paddle attachment, beat the Unsalted Butter (2 1/2 stick), Brown Sugar (1 cup) and Granulated Sugar (3/4 cup) on medium-high speed for 3 minutes, until light and fluffy.
On low speed, add the Egg (3) one at a time, scraping down the sides of the bowl after each addition, and then the Vanilla Extract (2 teaspoon). Mix until well combined.
In a small bowl, whisk together the All-Purpose Flour (2 1/2 cup), Corn Starch (2 teaspoon), Baking Soda (1 teaspoon) and Kosher Salt (1 teaspoon). With the mixer on low, add the dry ingredients to the butter and mix until just incorporated, then add the Semi-Sweet Chocolate Chips (2 cup) and mix until just combined.
Spoon the cookie batter onto the prepared sheet pan and using a spatula, spread it into one even layer that covers the entire surface of the pan. Bake for 12-14 minutes, until lightly golden brown and still soft to the touch. The cookie should seem under-baked. Cool completely.
Run a paring knife around the edges of the pan, then carefully invert the cookie onto a flat surface. Cut the cookie in half to form two equal-sized rectangles. Transfer one half to a large cutting board or flat platter that fits in your freezer, with the bottom side of the cookie facing up. Working quickly, spoon large scoops of Vanilla Ice Cream (1 1/2 quart) onto the cookie. Spread into an even layer, making sure the ice cream reaches the edges of the cookie.
Place the other cookie half, right side up, on top to form a giant sandwich. Press lightly, then transfer the board or platter to the freezer and freeze until firm, at least 3 hours or overnight.
Using a sharp knife, carefully trim about ¼-inch from each edge of the giant cookie sandwich, then cut it into 12 individual sandwiches. Place Mini Chocolate Chips (to taste) and Sprinkles (to taste) on small plates and press each side of the sandwiches into so the toppings adhere. Place all the decorated sandwiches back on the platter, freeze until firm, then serve or wrap individually with wax paper.