Rough chop ½ cup frozen raspberries into small pieces. Place in a freezer-safe bowl and return to the freezer immediately.
In a large bowl, whisk together the gluten free flour, baking powder, 1.5 tablespoons cornstarch, and salt. Set aside.
In a small bowl, stir together the 2 rounded tablespoons cornstarch and 3 tablespoons water until thin and watery. Set aside.
In a stand mixer with the paddle attachment, beat the butter and 1¼ cups sugar for 2 to 3 minutes until soft and creamy.
With the mixer on low, slowly add the cornstarch water mixture, milk, and cooled raspberry syrup. Mix until combined. Dough will look pink and chunky - that's correct.
Slowly beat in the flour mixture a little at a time until just combined.
If using food coloring, add 3 to 4 drops and mix until evenly blended.
Gently fold in the frozen chopped raspberries with a spatula. Do not overmix.
Cover the bowl with plastic wrap and freeze for at least 1 hour. Do not skip this step.