Assemble all ingredients and line an extra-large (15x21-inch) or 2 large sheet pans with parchment paper or silicone baking mat and set aside. Cut butter into 1 tablespoon pieces.
Mix butter, milk, sugars, salt, and cocoa in a medium pot over low heat, stirring often and scraping the pot's sides until butter melts.
After butter melts, raise heat to medium and stir until the mixture reaches a full boil, then continue to stir for one minute. Avoid under or over-boiling. Aim for 230°F if using a candy thermometer. Once done, remove from heat and stir for 10 seconds.
Stir in peanut butter until smooth, then mix in vanilla and oats, ensuring even coating.
Use a 2-tablespoon cookie scoop to place the cookie mixture onto the pan and let cool until hardened, about 30 minutes at room temperature or faster in the fridge.
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Notes
Note 1: Use unsweetened cocoa powder, not Dutch-processed cocoa powder.Note 2: Use creamy, not crunchy, peanut butter. I love Skippy® Creamy Peanut Butter. If you use natural peanut butter, mix well before measuring.Note 3: Most no-bake cookie recipes call for quick oats, which work great in this recipe. I like using 1-1/2 cups quick oats and 1-1/2 cups old-fashioned oats for more texture. You can use all old-fashioned oats for lots of chewiness.Storage: Store cookies at room temperature for 1 week, in an airtight container in the fridge for up to 2 weeks, or freeze for up to 6 months. To freeze, set cookies on a pan in the freezer until firm, then store in a freezer bag with parchment layers.