Strawberry Preparation: Begin by placing the freeze-dried strawberries into a high-speed blender or food processor. Pulse the berries until they achieve a fine, powdery consistency, akin to that of powdered sugar.
Strawberry Powder Allocation: Optionally, extract one teaspoon of the strawberry powder and reserve it for inclusion in the glaze. This step may be omitted if a plain glaze is preferred.
Dry Ingredient Mixture: Transfer the remaining strawberry powder into a medium mixing bowl. Add the all-purpose flour and whisk the components together to ensure they are thoroughly combined.
Creaming Process: In the bowl of a stand mixer equipped with the paddle attachment, combine the softened butter and powdered sugar. Beat these ingredients at a medium speed until the mixture is light and exhibits a fluffy texture, which should take approximately one minute.
Dough Formation: Reduce the mixer speed to low and gradually introduce the flour-strawberry mixture to the creamed butter and sugar. Continue to mix until the ingredients are fully amalgamated.
Final Mixing: Using a spatula, scrape down the sides of the bowl to reincorporate any stray ingredients, and then mix briefly to eliminate any remaining flour lumps.
Dough Chilling: Shape the dough into a disc and encase it tightly in plastic wrap. Refrigerate the wrapped dough for 15 minutes to firm.
Dough Rolling and Cutting: Once chilled, place the dough on a lightly floured surface and roll it out to a thickness of one-quarter inch. Utilize cookie cutters to shape the dough as desired and arrange the cutouts on a baking sheet lined with parchment paper.
Additional Chilling: Place the prepared baking sheet in the refrigerator for another 15 minutes, allowing the dough to chill further.
Baking: Preheat the oven to 350 degrees Fahrenheit. Bake the cookies for 15 to 17 minutes, or until the centers are just set, taking care to prevent excessive browning.
Glaze Preparation: While the cookies are baking, prepare the glaze by whisking together the powdered sugar and milk in a small bowl. Incorporate the reserved teaspoon of strawberry powder if using.
Decoration: Once the cookies have cooled, either drizzle them with the prepared glaze or dip them directly into it. If desired, sprinkle additional freeze-dried strawberry crumbs atop the glaze for decoration.
Setting: Allow the glazed cookies to set completely, which should take approximately 15 minutes, before serving or storing.