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 lightened and fluffy, about 3 minutes.
Mix in egg and egg yolk until well combined. Use spatula to scrape down sides as needed. Then, mix in vanilla extract.
In a small bowl, whisk together flour, baking soda, baking powder, salt, and cornstarch. Beat into butter mixture about 1/2 cup at a time. Scrape down sides as needed. Continue mixing until well combined.
Stir in mini semi-sweet chocolate chips and 1/4 cup of milk chocolate chips.
Press half of dough evenly into prepared baking pan. Spread peanut butter evenly around dough to within about 1/2 inch of sides of pan. Then spread remaining dough over the top of the peanut butter, gently pressing down at the edges of the 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.