Before beginning, line two cookie sheets with wax paper or parchment paper and set aside. Measure out your cookie butter, vanilla, and oats before beginning.
In a medium-sized saucepan, combine butter pieces, milk, brown sugar, and sugar. Place saucepan over low heat and stir¹ frequently until butter is melted.
Once butter has melted, increase heat to medium and stir constantly until mixture comes to a boil.
Stir constantly while boiling for one minute (I recommend using a timer! Boiling for too long or not long enough can negatively effect the outcome of your cookies, see post or notes² for more details).
Once one minute has passed, remove from heat. Add cookie butter and vanilla extract, stirring until cookie butter is completely melted and combined into mixture. Add oats and stir until completely coated in cookie butter mixture.
Drop cookies by about 1 1/2 Tablespoon-sized scoops onto prepared baking sheets.
Allow to cool completely (about 30 minutes) before serving and enjoying. The cookies will firm up as they cool.