Preheat oven to 325°. Grease a jelly roll pan (10"X15"X1").
Cream butter and sugars together for about 2 minutes with an electric mixer. Add peanut butter, eggs and vanilla and cream for another 2-3 minutes.
Add baking soda, salt and flour and mix just until combined. Stir in the oats.
Pour the batter into the prepared jelly roll pan. The batter will be thick so you will need to spread it evenly to fill the entire pan. I use a small rolling pin, but you can use your fingers or the back of a spoon.
Bake for about 13-15 minutes or until the edges barely start to turn a golden brown. Do not over bake or the bars will lose a lot of their moisture!
While the bars cool, you can make the frosting.
In a small saucepan, melt the butter, sugar and milk together over medium heat, stirring frequently. Bring to a boil and let it boil for 1 minute. Remove from heat and add the chocolate chips. Stir until the chocolate is completely melted and then add the marshmallows. Stir until the marshmallows are melted and then spread over the cooled bars. (The bars don't have to be completely cooled, but should at least sit for about 20-30 minutes before adding the frosting.)