Start by lining a rimmed baking sheet, that can fit into your refrigerator, with parchment paper.
In a large saucepan on medium heat, combine together the coconut oil, light brown sugar, oat milk, and unsweetened cocoa powder. Use a wooden spoon to gently stir the ingredients continuously until the ingredients have dissolved together.
Bump the heat down to medium low and continue stirring until the ingredients form a ball. Once a ball has formed you can stop stirring and allow the ball to boil for 90 seconds (undisturbed).
Once the ball has boiled for a minute and a half you can carefully remove the saucepan from the heat and stir in the remaining ingredients (peanut butter and vanilla extract).
When the mixture is smooth you can add the oatmeal (I would stir in half at a time, stirring between additions as the mixture will be stiff and you want the oats to be fully incorporated).
Use a small cookie scoop to scoop out the cookie dough, roll the dough between your hands to form a ball, and then flatten the ball on to the prepared baking sheet.
Place the cookies into your refrigerator to set for at least a half hour before serving.