In a large bowl, cream together the softened butter and granulated sugar with a stand mixer or hand mixer on medium speed until light and fluffy, about 2-3 minutes.

Beat in the egg and vanilla extract until well combined, scraping down the sides of the bowl as needed.

In a separate medium bowl, whisk together the all-purpose flour, baking powder, salt, and 1/4 cup of freeze-dried strawberry powder. Ensure the strawberry powder is fully incorporated and there are no large clumps.

Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix; overmixing can lead to tough cookies. The dough will be soft.

Divide the dough into two equal portions, flatten each into a disc, wrap tightly in plastic wrap, and refrigerate for at least 1 hour (or up to 2 days). This chilling is crucial for preventing the cookies from spreading too much.

Preheat your oven to 375°F (190°C). Line two baking sheets with parchment paper.

On a lightly floured surface (or between two sheets of parchment paper), roll out one disc of chilled dough to about 1/4 inch thickness. Use cookie cutters to cut out shapes, or simply cut into squares or circles with a knife.

Carefully transfer the cut-out cookies to the prepared baking sheets, leaving about 1 inch between each cookie.

Bake for 8-12 minutes, or until the edges are lightly golden and the centers are set. Baking time will vary depending on the size and thickness of your cookies. Avoid overbaking if you want soft cookies.

Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.

While the cookies are cooling, prepare the glaze. In a small bowl, whisk together the sifted powdered sugar, 2 tablespoons of milk (or lemon juice), and 1 tablespoon of freeze-dried strawberry powder until smooth. If the glaze is too thick, add more milk 1/2 teaspoon at a time until desired consistency is reached. If it's too thin, add a little more powdered sugar.

Once the cookies are completely cool, dip the tops into the strawberry glaze or drizzle it over them with a spoon. Place them back on the wire rack over parchment paper (to catch drips) and allow the glaze to set for about 30 minutes to 1 hour.