Preheat oven to 350°F (175 degrees C). Prepare a 9x13-inch baking pan with baking spray, parchment, or the butter/flour method.
In the bowl of a stand mixer (can also use hand-held mixer) beat the butter, brown sugar, and granulated sugar until well mixed, about 3 minutes.
Add in eggs one at a time, mixing well after each addition.
With mixer on low, add in the vanilla extract.
Remove bowl from stand mixer and add in salt, baking soda, baking powder, flour, rolled oats, plus semi-sweet chocolate chips. Stir by hand to moisten all ingredients.
Spread ½ mixture into the prepared baking pan. Pour milk chocolate chips on top of mixture. Carefully press the remaining cookie mixture on top of chocolate.
Bake in the preheated oven until golden brown, 30 to 40 minutes. (It shouldn't jiggle too much)
Let cool in the pan for about 5 minutes before cutting into bars.