In a large saucepan, combine the butter, sugar, non-dairy milk, and cocoa powder. Bring to a boil on medium heat, whisking frequently. Let boil for 1 minute.
Remove from heat. Immediately stir in the oats, peanut butter, vanilla, and salt.
Drop spoonfuls of the warm cookie mixture onto the baking sheets. A 1½-tablespoon cookie scoop works great for this.
Let cool at room temperture for 30 minutes or until set.