Combine butter and sugar and mix until creamy.
Add flavor & eggs and beat until fluffy
Add flour on a low speed, slowly
Put dough in refrigerator for a couple hours.
For thick large cookies bake at 375 for 10-14 mins (or until just set, do not wait for them to start browning)
For thin cookies, bake at 350 for 8-13 minutes.
As for the frosting.... I use the basic royal frosting recipe. Here is one from Food Network.
http://www.foodnetwork.com/recipes/alton-brown/royal-icing-recipe/index.html