Begin by removing 1 cup (2 sticks) unsalted butter and 2 large eggs from the refrigerator to allow them to reach room temperature.
Prepare Freeze-Dried Strawberry Powder: In a high-speed blender or spice grinder, process the freeze-dried strawberries until they become a fine powder. Mix this powder with 1/2 cup granulated sugar and store it in an airtight container until required.
Prepare Sparkling Strawberry Sugar: In a small bowl, combine 1 tablespoon freeze-dried strawberry powder with 1/2 cup sparkling sugar, mixing well. Store in another airtight container until ready for use.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Prepare Cookie Dough: In the bowl of a stand mixer, cream together 1 cup softened unsalted butter and 1 1/2 cups granulated sugar on medium speed for approximately 3 minutes, until light and fluffy. Add the eggs one at a time, blending thoroughly after each addition. Then, mix in 1 teaspoon pure vanilla extract, 1 teaspoon strawberry extract, and 1/2 teaspoon red gel food coloring until well incorporated.
In a medium bowl, whisk together 3 cups all-purpose flour, 2 tablespoons cornstarch, 2 teaspoons baking powder, 1 teaspoon baking soda, 2 teaspoons cream of tartar, ½ teaspoon salt, and 6 tablespoons freeze-dried strawberry powder. Gradually add this mixture to the wet ingredients, blending on low speed until just combined. Be careful not to overmix, as this could result in tough cookies. Chill the dough for at least 2 hours or up to overnight.
Place the Sparkling Strawberry Sugar in a separate small bowl. Using a medium cookie scoop, portion out 30 cookie dough balls. Roll each ball in your palms, then coat in the sparkling sugar mixture, ensuring they are evenly covered. Place the sugared dough balls on the prepared baking sheets, leaving at least 2 inches between each ball.
Bake the cookies in your preheated oven for about 10 minutes, until the tops are just beginning to set and appear slightly golden. Remove the baking sheets from the oven and allow the cookies to cool for 5 minutes before transferring them to a cooling rack to cool completely.
Once cooled, store the cookies in an airtight container at room temperature for up to 3 days, or in the refrigerator for up to 1 week. Enjoy these delightful, nostalgic treats!