Preheat an oven to 375 degrees F. and line a baking sheet with parchment paper.
Heat butter in a skillet until brown and it produces a nutty smell. (NOTE 1)
Allow the butter to cool and mix with the brown sugar and granulated sugar.
Add 1/2 egg and the vanilla extract and mix again.
Mix flour, baking soda, cinnamon and salt and add mixture to the butter/sugar mixture.
Add oats. (NOTE 2) and mix again. It has become a tough, sticky mixture.
Use a small ice scoop or 2 tablespoons and form your cookies. (NOTE 3)
Place the dough balls on your baking sheet and flatten with your hand. Place them about 2 inches apart.
Bake for 8-9 minutes for a more chewy cookie and about 10-12 minutes for a more crispy cookie.
Cook the cookies for a minute on your baking sheet and then move to a rack to cool completely.
Notes
When you brown the butter, stay with your skillet as the butter can easily burn. It does not take more than about a minute to create this foaming 'liquid' that produces a nutty flavor and will enhance the flavor of your oatmeal cookies.
As far as you oats are concerned, you can use only old fashioned rolled oats, only quick oats or a mix of the two. The more old fashioned oats, the more chewy the cookie.
The size of the cookie, obviously depends on how much dough you combine. Three tablespoons will form a 4-inch cookies and 1.5 tablespoons about a 2-inch cookie.