Step 1Melt butter and set aside to cool.
Step 2Place oatmeal in medium bowl. Stir in granulated and brown sugars and salt, and blend to break up any lumps. In separate bowl, whisk together melted butter, vanilla and egg. Stir into oatmeal mixture. Chill dough 20 minutes.
Step 3Roll dough into 1-inch balls and set on baking sheet lined with parchment paper. Flatten slightly with moist fingers.
Step 4Bake at 350 degrees until edges are nicely browned and tops of cookies are medium golden, 9 to 11 minutes. Cool well on baking sheet, about 10 minutes, before attempting to remove with metal spatula or icing knife. Cookies can also be brought to room temperature and flattened more to make them larger, more crisp and lacy-like. Cover loosely and keep refrigerated.