Melt the butter in the top of a double boiler. Stir in the sugar and add the chocolate.
Once the chocolate begins to melt slowly stir in the milk.
Cook for 4 - 5 minutes or until everything is melted together.
Turn off the heat and remove the top pan from the double boiler. Stir in the peanut butter, keep stirring until it's a creamy mixture.
Add the vanilla extract and the oats. Stir until the chocolate mixture is coating the oats.
Drop tablespoons of the mixture onto sheets of wax paper. You'll get about 2 dozen tablespoon sized cookies or a little less with bigger drops.
Let the cookies cool and set for 5 - 10 minutes if possible.