Cream together the butter and 1 cup of the sugar until smooth. Add eggs one at a time, mixing well after each, then stir in vanilla.
Add in flour and stir until dough forms.
In a small dish mix cinnamon and remaining sugar, set aside.
Grease your hands lightly, shape dough into 1 1/4 - 1 1/2" inch balls. Roll in the sugar cinnamon mixture to coat, then place on lightly greased baking sheet. Place cookies and the baking sheet in freezer for 10-15 minutes, this will prevent cookies from spreading out too much.
Bake at 375°F for 10-15 minutes, or until bottoms are lightly browned and tops are a bit firm.