How to prepare butter for baking when time is limited?
To get your butter up to room temperature faster, you can slice it into very small pieces or grate it with a cheese grater and then leave it out in a single layer. It will get where you want it in around 10 minutes that way.

You cookies taste better with room temperature butter because they have more air in them. When you mix the butter, sugar and eggs in your cookie recipe you're creating an emulsion of oil, proteins and air. Those little air pockets in the cookie dough then help the cookie puff up when it bakes. When the butter is melted all the way before you mix it in, this emulsion has much less air in it than it should, so your cookies' texture isn't as good.