Preheat oven to 350 degrees and very lightly grease a 10" cast iron skillet.
In your mixer with with paddle attachment, beat together 1/2 cup butter, 1/2 cup sugar, and 1/2 cup of brown sugar. Add in the 1/3 cup of peanut butter and whip ingredients together on medium speed until combined.
Next, add in the egg, 1/4 cup of milk, and 1/2 tsp of vanilla, continue mixing at medium-high speed until the color of the mixture lightens and turns fluffy about 3 minutes. You may have to scrape the sides to ensure the peanut butter is getting fully incorporated.
Finally, pour in 1 cup of oatmeal, 1 cup of all-purpose flour, and a 1/2 tsp of baking soda. Mix batter until everything is combined.
Using a rubber spatula, scrape the mixture into the cast iron skillet and evenly spread it around the pan.
Place on the middle rack of the oven and back for 30 minutes, or until golden brown and the sides and middle have risen. If poked in the middle with a toothpick, the toothpick should come out clean.