Pulse the rolled oats in a food processor until slightly broken down but not powdered. Then grind freeze-dried strawberries into a fine powder for flavor and color. Set both aside before moving forward with the dough.
In a large bowl, whisk together the oats, flour, baking powder, baking soda, salt, and strawberry powder. This ensures the fruit flavor is evenly distributed throughout the dough. Mix gently so the dry ingredients stay light and well combined.
In another bowl, whisk melted butter with both sugars until smooth and glossy. Add the egg, egg yolk, and vanilla extract, mixing until fully incorporated. The mixture should look creamy and slightly thick.
Slowly combine the wet ingredients with the dry mixture. Stir just until combined to avoid overmixing. Chill the dough briefly to make it easier to scoop.
Scoop dough onto lined baking sheets, spacing them apart. Bake until edges are set but centers remain soft. Let cookies cool slightly before glazing.
Whisk powdered sugar, strawberry powder, milk, corn syrup, and vanilla until smooth. Dip the tops of cooled cookies into the icing. Let them sit until the glaze fully sets.