Preheat oven to 350 degrees. Line a large baking sheet with parchment.
In a bowl, cream the butter, brown sugar, and sugar until light and fluffy, about 3-4 minutes. Whip in the eggs, one at a time, then the vanilla. Add the oats, flour, baking soda, and salt. Mix until just combined. Do not overmix. Do not, I repeat do not.
Scoop rounded 2 tablespoon sized mounds of dough. Roll into a ball. Place onto the prepared baking sheet, taking care not to overcrowd the pan.
Bake for 10-12 minutes until the edges are set but the centers are still soft. Cool on the baking sheet.
Line a sheet of parchment beneath a wire cooling rack. In a bowl, whisk together the powdered sugar, maple syrup, vanilla, and 1 tablespoon of milk. The glaze should be glossy but not overly runny. Dunk the top of each cookie lightly into the glaze and invert onto the wire rack so the unglazed side is sitting on the metal.
Eat a few right away, or cool completely and store in an airtight container for up to 5 days, the fridge for a week, or the freezer for infinity (3 months).