Preheat oven to 350°F and grease a pan. (See notes for size options)
In the bowl of a stand mixer, cream the butter, brown sugar and sugar.
Stir in the eggs and vanilla.
Add the flour, baking soda and oats and mix until combined.
Spread the mixture in the prepared pan and bake. (See notes for times, depending on pan size used)
While the bars are in the oven, make the frosting.
Place the butter in a saucepan and cook on medium heat until it turns light brown.
Remove from the heat immediately and stir in the powdered sugar and vanilla.
Add milk 1 teaspoon at a time until you have a nice spreading consistency.
Pour the icing over the warm bars and spread.
Let cool then cut into bars and enjoy!