Preheat oven to 350°F (177°C). Line 3 large baking sheets with parchment paper or silicone baking mats. (If you don’t have 3 baking sheets, bake the cookies in batches.)

Whisk the flour, cornstarch, baking soda, and salt together in a medium bowl.

Using a handheld or stand mixer fitted with a paddle attachment, beat the butter, brown sugar, and granulated sugar together in a large bowl on medium-high speed until combined and creamy, about 2 minutes. Add egg, egg yolk, and vanilla extract, then beat on medium-high speed until combined. Scrape down the sides and up the bottom of the bowl as needed. Beat in the dry ingredients on low speed, then beat in the chocolate chips until combined. The dough will be soft and sticky.

Since the dough is so sticky, I recommend using a cookie scoop and this medium size is perfect. Scoop cookie dough into balls, about 1.5 Tablespoons of dough per cookie, and arrange 3 inches apart on the baking sheets. Bake for 12–13 minutes or until lightly browned on the sides. The centers will look soft.

Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes. If desired, while the cookies are still warm, press extra mini chocolate chips into the tops of the cookies. This is optional and just for looks. Transfer to a wire rack to cool completely before assembling your ice cream sandwiches.

Assemble the sandwiches: Flip a cooled cookie over and place 1 generous ice cream scoop, about 1/4 cup or 45g, on top. Use your scoop to gently spread the ice cream to the edges. Sandwich a cookie on top, then pick up the assembled sandwich and gently press it all together in the very center to make a compact sandwich. Roll sides into mini chocolate chips, sprinkles, or nuts. If not enjoying right away (they’re messy if you don’t freeze them first), immediately wrap assembled sandwich in plastic wrap or parchment paper and place in the freezer. Repeat with remaining cookies and ice cream.

Freeze for at least 3 hours and up to 3 months.