Preheat oven to 325°F.
In a large bowl, cream butter, sugar, and vanilla.
Stir in flour and peanuts.
Pinch off pieces of dough the size of a small walnut; place on ungreased cookie sheet.
Bake about 20 minutes.
Cool on cookie sheet for 1 to 2 minutes; transfer to wire cooling racks.
Roll in granulated sugar while still warm.