Preheat oven to 350°F (175°C).
In a large mixing bowl, cream together the butter, brown sugar, and granulated sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, cinnamon, and salt. Gradually add to the creamed mixture and mix well.
Stir in the oats until just combined.
Drop by rounded tablespoonfuls onto ungreased baking sheets.
Bake for 10-12 minutes, or until the edges are golden brown. Cool on baking sheets for 1 minute before removing to wire racks to cool completely.
For the icing, combine the powdered sugar, milk, and vanilla extract in a small bowl. Drizzle over cooled cookies.