Well butter or grease a 12-cup muffin tin or line it with liners.
In a large bowl, whisk together 2 ¼ cups gluten free flour , ½ cup granulated sugar, 3 teaspoons baking powder, ½ teaspoon fine sea salt, and ½ teaspoon ground cinnamon if using. Set aside ¼ cup of this dry mix.
Make a well in the center and stir in the ¼ cup unsalted butter, 1 egg, and 1 cup whole milk. Stir together until just combined. Toss the reserved dry mix with the blackberries.
Gently fold in the 1 cup fresh or frozen blackberries, then divide the batter equally between the muffin cups. Let the batter rest for about 20 minutes. Preheat the oven to 375℉
When the oven is preheated and the batter has rested, place the tin in the oven and bake for 20-25 minutes, until a tester inserted in the center of a muffin comes out clean.
Remove from oven and let cool in pan 5 minutes, then turn out onto a wire rack to cool 10-15 minutes more.
Notes
Don't thaw the berries. If you use frozen blackberries, don't thaw them before adding them to the batter. If the berries defrost too much they will add too much moisture to the muffins.
Rest the batter. Let the batter rest for up to 20 minutes before baking so that the gluten-free flour hydrates, leading to a better texture.
Try brown sugar. Instead of granulated sugar, try light or dark brown sugar. Coconut sugar also works.
Dairy-free: Substitute your favorite non-dairy butter and non-dairy milk.
Egg-free: I haven't made these without an egg, but you could try a flax egg instead of the egg and it should work well.