Preheat oven to 350°F. Grease and flour baking sheets
Cream butter and sugar. Add vanilla;
Stir in flour and oats.
Drop batter by the tablespoon onto prepared baking sheets leaving plenty of room for cookies to expand - at least 3-4 inches. Flatten dough slightly with spoon or fingertips.
Bake until cookies flatten and brown, about 10 minutes.
Let cookies cool for 4 to 5 minutes on baking sheets. Lift from baking sheet with spatula to cooling racks to cool completely