This is my favorite butter cookie. It's by Alice Medrich. It's very much like the one that Bunnee linked, but there's no baking powder. Letting it sit overnight is key. I can never wait, so I always slice one off the day of after several hours. They're much better the next day. I roll them in Demerara sugar before baking for a fun crunch.
I've never had a butter cookie from an Italian bakery, but this recipe from Melissa Clark is amazing. Be sure to use cultured butter if you try it. http://cooking.nytimes.com/recipes/1015209-cultured-butter-cookies
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http://www.food.com/recipe/worlds-best-butter-cookies-50684