2½ sticks (10 ounces) unsalted butter, at room temperature, plus more for greasing the pan
1 cup light brown sugar, lightly packed
¾ cup granulated sugar
2 large eggs + 1 large egg yolk, at room temperature
2 teaspoons vanilla extract
2½ cups all-purpose flour
2 teaspoons cornstarch
1 teaspoon baking soda
1 teaspoon kosher salt
2 cups semisweet chocolate chunks or chips (about 12 ounces)
1 (1.5 quart) container vanilla ice cream
Sprinkles and mini chocolate chips, for decorating
Preheat the oven to 350 degrees. Grease an 18x13x1-inch sheet pan with butter or nonstick-spray and line with parchment paper, leaving an inch or two of overhang on two sides on the pan.
In an electric mixer fitted with the paddle attachment, beat the butter and both sugars on medium-high speed for 3 minutes, until light and fluffy. On low speed, add the eggs and egg yolk one at a time, and then the vanilla. Mix until well combined.
In a small bowl, whisk together the flour, cornstarch, baking soda, and salt. With the mixer on low, gradually add the dry ingredients and mix until just incorporated, scraping the sides of the bowl with a spatula if necessary. Add the chocolate chips and mix until just combined.
Dollop the cookie dough onto the prepared sheet pan in big spoonfuls, covering as much of the pan as possible. Holding the parchment paper with one hand, and a spatula with the other, spread the dough into an even layer that covers the entire surface of the pan.
Bake for 13 to 16 minutes, until lightly golden brown and still soft to the touch. The cookie should seem slightly under-baked. Cool completely in the pan.
Run a paring knife around the edges of the pan, then lift the parchment paper and carefully move the giant cookie onto a large cutting board. Cut the cookie in half crosswise to form two equal-sized rectangles. Chill the cookie halves until firm, at least 30 minutes.
When ready to assemble the sandwiches, remove the ice cream from the freezer and let it sit at room temperature for 10 to 15 minutes, until slightly softened.
Place one half of the cookie, bottom-side up, on a cutting board or flat platter that fits in your freezer. Working quickly, spoon large scoops of ice cream onto the cookie. Spread into an even layer, making sure the ice cream reaches the edges of the cookie. Freeze for at least 30 minutes, then place the other cookie half, right side up, on top to form a giant sandwich. Press lightly, then 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 and sprinkles on small plates and press each side of the sandwiches into so the toppings adhere. Using a pastry brush, brush the excess sprinkles or chocolate chips from the sides of the sandwiches so only the ice cream is covered.
Freeze sandwiches until firm, then serve or wrap individually with wax paper and store for up to 2 weeks in the freezer.
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