Continue cooking, stirring constantly and watching closely, until butter JUST starts to turn golden (5-8 minutes)
Butter will be foamy and bubble
Immediately remove from heat and cool for 15 minutes
Combine 1/2 C browned butter and all remaining cake ingredients in large bowl Set aside remaining browned butter for frosting.
Beat at low speed 30 seconds. Increase speed to medium; beat, scraping bowl occasionally until well mixed - about 2 minutes
Pour batter into greased 9x13 pan and bake for 30-35 minutes or until a toothpick comes out clean Cool completely
Combine remaining browned butter, powdered sugar and vanilla in small bowl
Beat at medium speed gradually adding enough milk for desired spreading consistency
Frost cooled cake
Notes
Bring your chilled ingredients (such as butter, eggs and milk) to room temperature. There is an actual scientific reason for this. Warm ingredients mix together easier and quicker which prevents you from overmixing things. In this case since we are melting the butter it does not need to be at room temperature but bring your eggs to room temperature.
Mix ingredients together just until you don't see any more dry ingredients. Use a spatula to scrape down the sides of your bowl to finding anything that might be hiding.
I always set my timer for five minutes before the stated recipe time. This helps avoid over baked cake. Insert a toothpick to make sure cake is cooked through. The cake will also be dry to the touch and bounce bake when you touch it.
For cupcakes you will bake them for 18-20 minutes. Mini cupcakes will bake for 10-12 minutes.