Preheat oven to 350 degrees. Line bottom of a 10" round baking pan with parchment paper. Butter and flour sides of pan (or use Baking PAM).
In a large bowl, use electric mixer to beat butter, sugar, and brown sugar until light and fluffy, about 3 minutes.
Beat in egg and egg yolk until well combined. Use spatula to scrape down sides as needed. Next, beat in vanilla extract.
In a small bowl, whisk together flour, baking soda, baking powder, salt, and corn starch. Beat into butter mixture about 1/2 cup at a time. Scrape down sides as needed. Mix until well combined.
Stir in mini semi-sweet chocolate chips and 1/4 cup of milk chocolate chips.
Press dough evenly into prepared baking pan. Gently press remaining 2 tbsp of milk chocolate chips into top of dough (place chips randomly throughout the top to look more natural).
Bake for 21-24 minutes, or until top is golden brown and center no longer wiggles.
Remove from oven. Let cool completely before removing from pan.