Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone mats.

In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract until evenly combined.

In another bowl, whisk together the flour, baking soda, cinnamon, and salt. Gradually add this dry mixture to the wet mixture, mixing until just combined.

Fold in the rolled oats until they are evenly distributed throughout the dough.

Drop spoonfuls of dough onto the prepared baking sheets, leaving space between each cookie for spreading.

Bake for 12 to 15 minutes, or until the edges turn golden brown. The centers may look slightly underbaked.

Once baked, allow the cookies to cool on the baking sheets for 5 minutes, then transfer them to wire racks to cool completely.

To make the icing, whisk together the confectioners' sugar, milk, and vanilla extract in a bowl until smooth and glossy.

Once the cookies are completely cooled, drizzle the icing over the tops using a fork or a piping bag.

Let the icing set before serving.