Melt the butter in a 3 1/2-quart saucepan over medium heat. Stir in the sugar and milk and bring to a boil; boil for 1 1/2 minutes.
Remove from the heat and immediately stir in the oats, peanut butter, vanilla and salt, stirring to combine. Add the chocolate, stirring until just combined.
Drop the dough by rounded tablespoonfuls on the prepared baking sheets. Let the cookies stand until set, about 30 minutes.