Place the oats in a food processor and pulse about 10 times or so to break down but not fully pulverize. You want some texture throughout still. Transfer to a large mixing bowl and set aside.
Add the freeze-dried strawberries to the food processor and pulse until it forms a powder. Reserve about 2 tablespoons for the glaze, and then add the rest to the bowl with the oats.
To the bowl of oats and strawberry powder, add the flour, baking powder, baking soda, salt and cinnamon. Give it a good whisk and then set off to the side.
In the bowl of a stand mixer, beat together the softened butter, strawberry jam and food coloring (if using) until light and fluffy, about 3 minutes. Add the sugars and beat on medium speed until light and airy, about 5 minutes. Beat in the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract. Then add the dry ingredients and mix until well combined. Cover the bowl and chill the dough for at least 1 hour.
Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
Once dough has chilled, use a small cookie scooper to scoop out the dough onto the prepared baking sheets, about 6 per sheet. Space out evenly to allow space for spreading. Bake until lightly golden brown around the edges and just about fully set in the center, about 12 to 14 minutes. Remove from the oven and give the baking sheets a few gentle taps on the counter to flatten out the cookies slightly. Allow to cool for 5 minutes on the baking sheets before transferring to a wire rack to cool completely.
For the glaze, in a shallow bowl, whisk together the powdered sugar, reserved strawberry powder, and as much of the milk as needed to create a smooth pourable glaze. If it's too thick, add a splash or two more of milk.
Once the cookies have cooled completely, carefully dip the tops into the glaze to create a crackly coating on top. Return to the wire rack and allow to set before serving. Enjoy!