Add freeze-dried strawberries to a food processor and pulse until you have a fine, even powder with no large chunks. Set aside.
Preheat oven to 350°F (177°C). Line two baking sheets with parchment paper or silicone baking mats.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt. Add strawberry powder and whisk again until evenly combined.
In a large bowl with a stand or hand mixer, beat softened butter, granulated sugar, and brown sugar on medium-high speed for 2-3 minutes until light, fluffy, and pale in color.
Add the egg, egg yolk, and vanilla extract. Beat until fully combined, scraping the bowl as needed. Add food coloring if using and mix until even.
Reduce mixer speed to low and add dry ingredients in two additions, mixing just until incorporated with no dry streaks remaining. Do not overmix.
Place remaining 1/4 cup granulated sugar in a small bowl. Using a cookie scoop, portion dough into 1.5 tablespoon balls. Roll each ball in sugar until coated and place on baking sheets 2 inches apart.
Bake one sheet at a time on the middle rack for 10-12 minutes until edges are set and centers look slightly underbaked. For crackly tops, drop baking sheet firmly onto counter once or twice after removing from oven.
Let cookies rest on baking sheet for 5 minutes to finish setting, then transfer to a wire cooling rack to cool completely before storing.