Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, cream together the softened butter, granulated sugar, and brown 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, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Fold in the rolled oats until evenly distributed.
Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake for 12–15 minutes, or until the edges are lightly golden. Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.
While cookies bake, prepare the icing by combining milk, granulated sugar, vanilla extract, and almond extract (if using) in a small bowl. Whisk until smooth, then gradually add powdered sugar until desired consistency is reached.
Once cookies have cooled completely, spread or drizzle the icing over each cookie.
Let the icing set for at least 30 minutes before serving. Store in an airtight container at room temperature.
Notes
These cookies stay fresh at room temperature for up to 5 days when stored in an airtight container.