Preheat the oven to 325°F (165°C) and line a sheet pan with parchment paper.
In a medium bowl, whisk together the gluten-free flour, cornstarch, garlic powder, and salt until evenly combined.
Add the shredded cheddar, cold cubed butter, and cold water to the dry ingredients.
Use a pastry cutter (or two forks) to cut the butter and cheese into the flour mixture until pieces are no larger than a pea.
Begin kneading the mixture in the bowl until it starts to come together; form a ball and transfer to a lightly clean work surface.
Knead until smooth and easy to work with, adding up to 1 teaspoon more water if the dough cracks or a little extra flour if it becomes sticky.
Place the dough between pieces of parchment and roll into an even square about 1/8 inch thick, flipping the dough occasionally to keep the parchment smooth.
Trim the edges with a thin blade to square the dough, then cut into 1-inch squares with a pizza cutter or knife.
Transfer squares to the prepared baking sheet spacing them apart, reroll scraps to make more crackers as needed.
Poke a small hole in the center of each cracker with a toothpick or skewer to help them bake evenly.
Bake at 325°F for 14–16 minutes, until edges begin to turn golden brown.
Remove from oven and let the crackers cool completely on the pan before serving or storing.