Preheat oven to 375º F. Line baking sheets with parchment paper or silicon baking mats. Set aside.
Heat butter and brown sugar in a 2-quart saucepan over medium heat, stirring frequently with a wooden or silicon spoon, until butter has melted and mixture is smooth. Stir in oats, flour, salt, egg, and vanilla.
Drop cookie batter by the teaspoon onto prepared baking sheets, leaving at least 2 inches between each cookie to allow them to spread.
Bake for 5 -7 minutes, watching closely to prevent them from over-baking. The lace cookies should be golden brown.
Allow to cool on the cookie sheet for 30 seconds and remove onto racks to cool completely.
Store in an airtight container.
Make sure to use real butter and not margarine as it will impact the results of the cookies.Make Ahead Tips You can prepare the dough and store in an airtight container in the refrigerator for 3 to 5 days. When you are ready to bake, drop the dough by teaspoons onto parchment lined baking sheets 2 inches apart and follow the recipe baking instructions.Freezing Oatmeal Lace Cookie dough: Drop dough by teaspoons onto a parchment covered baking sheet. Cover and place in the freezer for 1 hour or until the dough is frozen. Remove from the freezer and place the cookie mounds into airtight containers or freezer bags. Label the bag with the date and name of the cookies.When you are ready to bake the cookies, remove the container from the freezer. Remove the number of cookies from the container that you wish to bake and place them at least 2 inches apart on a parchment lined baking sheet. You will not need to thaw the dough before baking. Bake as directed in your recipe but you will probably need to add a couple of extra minutes to the baking time.Storing baked cookies: Cool the baked cookies thoroughly. Layer cookies between pieces of parchment of waxed paper and place into an airtight container. These cookies should keep up to 1 week.