Place a medium saucepan on the stove and melt the butter over medium heat, watching it turn silky and smelling rich as it melts completely.
Add the sugar, cocoa powder, and milk to the melted butter. Stir constantly with a spatula until the mixture is smooth, glossy, and begins to bubble gently, about 2-3 minutes.
Bring the mixture to a gentle boil and set a timer for 1 minute. Keep stirring during this time to help the sugars dissolve and the mixture thicken slightly.
Remove the pan from heat and immediately stir in the vanilla extract. Then add the rolled oats and stir thoroughly until the oats are evenly coated and the mixture is thick and fudgy.
Line a baking sheet with parchment paper. Use a spoon or cookie scoop to drop dollops of the mixture onto the parchment, spacing them about 2 inches apart. Gently flatten each dollop with the back of the spoon.
Place the tray in the refrigerator and chill for at least 30 minutes, allowing the cookies to firm up and set with a shiny, crackled top.
Once the cookies are firm, peel them gently from the parchment paper and serve immediately, or store in an airtight container for up to a week. These cookies are best enjoyed slightly chilled, with the chocolate aroma filling the room.