Preheat the oven to 350°F (175°C).

In a 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, then stir in the vanilla extract.

In another bowl, whisk together the flour, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Fold in the oats and chopped strawberries.

Drop tablespoon-sized balls of dough onto a baking sheet lined with parchment paper, spacing them about 2 inches apart.

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.

Remove from the oven and let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

In a small bowl, whisk together the powdered sugar, milk, and strawberry puree until smooth.

Once the cookies are completely cool, drizzle the icing over the top of each cookie.