Preheat your oven to 350°F and line a baking sheet with parchment paper or silicone baking mat.
In a medium bowl, combine butter, brown sugar, granulated sugar, and peanut butter, and beat until light and fluffy.
Add egg yolk, milk, and vanilla, and beat until well-combined.
Add flour, baking soda, salt, and oats. Use a wooden spoon to stir until a sticky dough forms.
Drop golf-ball-size spoonfuls of dough onto the baking sheet as far apart as possible—these cookies will spread.
Bake for 12 to 15 minutes, until the tops of the cookies look set.
Cool on the baking tray for at least 10 minutes. Serve and enjoy!