Line two baking sheets with parchment or wax paper and set them near the stove. Measure the quick oats into a bowl and measure the peanut butter, vanilla, and salt so they are ready to add the instant the boil finishes.
Add the diced butter, sugar, milk, and cocoa powder to the saucepan. Place over medium heat and stir until the butter melts and the cocoa dissolves into a smooth, dark liquid.
Raise the heat to medium-high and stir until the mixture reaches a full rolling boil, bubbling across the entire surface and not just at the edges. Clip or dip a thermometer into the pan at this point if you have one.
Once the boil is rolling, start a timer and boil for exactly 60 seconds, stirring gently the whole time so the bottom does not scorch. If using a thermometer, pull the pan the moment it reads 230°F (110°C).
Remove the pan from the heat immediately. Stir in the peanut butter, vanilla, and salt until the peanut butter melts completely and the mixture looks smooth and uniform.
Add all 3 cups of quick oats at once. Stir quickly and firmly until every oat is coated in the chocolate mixture.
Working fast before the mixture sets in the pan, scoop rounded tablespoons (about 1.5 to 2 tablespoons each) onto the lined sheets. They do not spread, so you can fit them close together.
Leave the cookies undisturbed at room temperature for 20 to 30 minutes until firm to the touch. Once set, peel them off the paper and serve.