Lay a large sheet of parchment paper or wax paper on the counter. This is where the cookies will cool and set.
In a medium saucepan over medium-high heat, combine the milk, butter, granulated sugar, and brown sugar. Stir occasionally until the butter is melted and everything is well combined.
Once the mixture comes to a full rolling boil, stop stirring. Continue boiling until the mixture reaches 234–240°F on a candy thermometer (soft-ball stage), about 1-2 minutes of steady boiling. This step ensures the cookies will set properly.
Remove from heat. Stir in the peanut butter, vanilla, and salt until smooth.
Add the rolled oats and stir until evenly coated and thickened.
Drop heaping tablespoons of the mixture onto the prepared paper. Allow to cool and set at room temperature for 20–30 minutes, until firm. Enjoy!