Line two baking sheets with wax paper and set aside.
In a large saucepan over medium heat, combine the granulated sugar, milk, and butter. Bring to a boil, while stirring consistently. It should be a roaring foamy boil before you move on to the next step. If it doesn't come to a roaring boil here, the final cookie won't set.
Once it has come to a roaring boil, boil for one minute while continuing to stir. If it doesn't boil at a roaring boil for one minute, the final cookie won't set.
Remove from heat and stir in the oats, peanut butter, and vanilla.
3 cups old fashioned oats, 1 cup creamy peanut butter, 1 tablespoon vanilla extract
Using a large spoon or cookie scoop, scoop the mixture onto the waxed paper. Allow to cool completely. Eat immediately or store in an airtight container for up to a week.
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Notes
I highly recommend avoiding Kirkland brand butter for this recipe. While it may work great with some baking recipes, in my experience it has too high water content to work in this recipe and will result in cookies that don't set.