Preheat the oven to 350 F. In a large bowl, combine butter with sugar until fluffy. Add in the vanilla extract and flour, and mix until combined.
Roll the cookie dough into balls, and flatten each one slightly. Place one mini Reese's peanut butter cup on each piece of dough. Roll into a ball, covering it fully. Bake for 10-12 minutes.
Place the powdered sugar into a shallow dish. Roll the baked cookies into the powdered sugar.