You need to work quickly at the end, so first measure out the peanut butter into a small bowl and set aside. Next, measure out the oats and place into a medium bowl. Set aside.
Pour the sugar, butter, milk, cocoa into a medium-sized (4-quart) pot, then heat over medium-high heat, stirring occasionally to mix together. Once the mix comes to rolling boil, let it boil for exactly 1 minute.
Working quickly, remove the pot from the heat and add peanut butter, stirring to melt it into the hot sugar mixture. As soon as it's melted in, stir in the oats. Continue stirring to help the mixture cool, then add the vanilla, and stir to incorporate. The mixture will thicken up.
Place a large sheet of parchment paper or aluminum foil on the counter. Using a large spoon or pair of teaspoons, place rounded heaps of the cookies onto the parchment/foil. Let the cookies rest about 15-30 minutes, during which time they'll harden enough to serve.
Best eaten the day they are made, these cookies will dry out as time goes on and become a little crumbly. If you have leftovers, they'll keep for several days in an airtight container or for 2 months in the freezer.