Preheat oven to 325°F. Spray a 9-inch cast-iron skillet with cooking spray.
In a large bowl, use an electric mixer to beat 10 tablespoons softened butter and 1 cup firmly packed light brown sugar until light and fluffy, about 2–3 minutes.
Add 1 large egg, 1 egg yolk, and 1 teaspoon vanilla extract; beat until combined.
In a separate bowl, whisk together 3/4 cup all-purpose flour, 1 teaspoon baking soda, and 1/4 teaspoon salt. Add the dry mixture to the butter mixture and beat just until incorporated—do not overmix.
Stir in 3/4 cup of the 1 cup old-fashioned oats and 1/3 cup of the 2/3 cup semi-sweet chocolate chips. Reserve the remaining 1/4 cup oats and 1/3 cup chocolate chips for topping.
Press half of the cookie dough evenly into the bottom of the prepared skillet.
Spread all of the 2/3 cup creamy peanut butter in an even layer over the dough in the skillet.
Drop the remaining half of the dough by spoonfuls over the peanut butter and gently spread or press to cover as much as possible.
Evenly sprinkle the reserved 1/4 cup oats and reserved 1/3 cup chocolate chips over the top of the dough.
Bake for 45 minutes in the preheated oven. If the top begins to brown too much, loosely cover the skillet with aluminum foil. Remove from oven and let the skillet cookie cool before slicing.