In a large bowl, whisk together the gluten-free flour, 1½ tablespoons cornstarch, baking powder, and kosher salt. Set aside.
In a small bowl, stir together 2 rounded tablespoons cornstarch with 3 tablespoons water until thin and watery. Set aside.
In a stand mixer with the paddle attachment, beat the butter and 1¼ cups sugar together on medium speed for 2–3 minutes until light and creamy.
With mixer on low, slowly add the cornstarch water mixture, milk, and cooled raspberry syrup. Mix until combined (dough may look pink and chunky - this is normal).
Slowly add the flour mixture, a little at a time, until just combined.
Add 3–4 drops red food coloring if using, and mix until evenly blended.
Fold in the frozen chopped raspberries gently with a spatula. Do not overmix.
Cover bowl with plastic wrap and freeze for at least 1 hour. Do not skip or substitute the fridge - it must be the freezer.