Preheat oven to 325°F. Prepare baking sheets with silicone baking mats or parchment paper. Combine and stir flour, cornstarch, baking soda, and salt together in a medium bowl. Set aside.
Using a handheld or stand mixer fitted with a paddle attachment, beat the butter, brown sugar, and granulated sugar together on medium speed until light in color and creamy, about 2 minutes.
Add egg, egg yolk, and vanilla extract, then increase speed to medium-high speed until combined. Scrape down the sides of the bowl as needed.
Slowly add in the dry ingredients on low speed, then add in the mini chocolate chips until combined. The dough will be thick; you may need to stir in the chocolate chips in by hand.
Divide dough into 8 portions. Shape each into a rounded, tall mound. Press a few additional chocolate chips onto the tops of dough mounds if desired. Place 3-4 on a baking sheet with plenty of room to spread out. Finished cookies will be about 5-6 inches in diameter.
Bake for 20 minutes until golden and the center is set or until edges and top are lightly browned. I like to check at 15 minutes as oven temperatures can vary. It is important to let the cookies remain on the baking sheet for 15-20 minutes after removing from the oven to cool. The cookies will finish baking as they rest.
Transfer to a wire rack to cool completely. Store in an air-tight container for up to 1 week.