Preheat oven to 350°F. Line baking sheets with parchment paper or silicone baking mats.
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