Meanwhile, for frosting, heat butter in a large saucepan over medium heat until boiling. Let the butter turn a delicate brown and remove from heat.
Add powdered sugar, vanilla extract and milk. Whisk together until smooth (it should be thicker than a glaze but thinner than frosting). Using a spatula, spread the brown butter frosting over the warm bars (the frosting will be easier to spread while the cake is still warm.)
Rockport resident Heather Atwood writes the Food for Thought column weekly. Questions and comments may be directed to firstname.lastname@example.org. Follow her blog at HeatherAtwood.com.