Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 10x15-inch baking pan.
Cream white sugar, brown sugar, and butter together in a bowl. Mix in peanut butter and eggs until smooth. Stir in oats, baking soda, and vanilla extract. Add chocolate chips and milk chocolate pieces. Spread in the greased baking pan.
Bake in the preheated oven until lightly brown on top, about 15 minutes. Be careful not to overbake.