Prep. Preheat oven to 375ºF. Lightly grease a cookie sheet with cooking spray and set aside.
Mix the wet ingredients. In your mixer's bowl, combine butter and brown sugar; mix until light and fluffy. Beat in eggs and vanilla.
Add the dry ingredients. With a wooden spoon, mix in the remaining ingredients (apart from the powdered sugar and milk). Stir until just blended.
Bake. Drop rounded tablespoonfuls of dough about 2 inches apart onto prepared cookie sheets. Bake for 10 to 12 minutes, or until set. Remove from oven and transfer the cookies to a cooling rack.
Make the glaze. Meanwhile, mix powdered sugar and water (or milk) in a small mixing bowl for the glaze. Drizzle the glaze over the cooled oatmeal cookies.