For the Raspberry Syrup:
In a saucepan over medium heat, cook ¼ cup granulated sugar and 1 cup frozen raspberries. Stir constantly until broken down and syrupy, about 10 minutes. Strain through a mesh colander into a bowl and let cool. You should have 2-3 tablespoons of syrup.
For the Cookies:
Measure ½ cup frozen raspberries and chop them into small pieces. Return them to the freezer while you prepare the dough.
In a large bowl, whisk together the gluten-free flour, cornstarch, baking powder, and kosher salt. Set aside.
Mix the remaining cornstarch and water in a small bowl until it forms a thin, watery mixture.
In the bowl of an electric mixer, beat the butter and 1 ¼ cups of sugar until soft and creamy (about 2-3 minutes). Slowly add the cornstarch mixture, milk, and cooled raspberry syrup. Beat until combined.
Gradually add the dry ingredients to the wet ingredients until just combined.
If using, add the red food coloring and gently fold in the chopped raspberries, creating a marbled effect.
Cover the dough with plastic wrap and freeze for at least 1 hour.
Preheat the oven to 325°F (160°C) and line a baking sheet with parchment paper.
Scoop dough using a large cookie scoop, roll each ball in the extra 2 tablespoons of sugar, and place them on the baking sheet.
Bake for 15 minutes. Immediately reshape cookies with a spatula if necessary and let them cool on the sheet for 5 minutes before transferring to a cooling rack.