In a large bowl, combine the oats, peanut butter, vanilla, and salt. Set it aside while you boil the sugar.
In a small saucepan, combine the vegan butter, sugar, and water. Start to bring the mixture to a boil. As soon as the edges of the mixture are bubbling all the way around the pan, set a timer for 2 minutes and 30 seconds. Let the mixture boil without stirring until the timer goes off.
When the timer goes off, immediately remove the boiled sugar from the heat and pour it into the bowl of oats. Stir well to make sure everything is evenly coated.
Use a heaping tablespoon to scoop the dough onto a baking sheet lined with parchment paper. Use the back of the spoon to flatten the cookies. You can let the cookies cool at room temperature, or speed the process by placing them in the fridge or freezer.
These cookies should be firm at room temperature, but if for some reason they are softer to the touch, you can store them in the fridge and they'll remain firm that way. My husband prefers these cold, so we keep them in the fridge so they'll last longer anyway! They can be stored at room temperature for up to a week, but they do start to dry out the longer they stay out on the counter.