Begin by preheating the oven to 400°F. Line a large baking sheet with parchment paper.
In a large bowl, combine the gluten-free flour, baking powder, salt, garlic powder, mustard powder, and cayenne. Lightly stir together with a fork.
Place the cold butter cubes in the bowl of dry ingredients. Toss to coat them in flour, then use your hands or a pastry cutter to break apart the butter pieces and blend them into the flour. Keep cutting the butter into the flour until the pieces are small and the mixture looks like sand. Work quick to avoid the butter melting.
Next, add the shredded cheddar to the mixture and stir around with a fork to ensure it's evenly incorporated.
In a separate small bowl, beat together the eggs and milk. Pour into the large bowl. Begin to mix together with a fork or wooden spoon. Once the wet ingredients are mostly incorporated, turn the dough out onto the counter. Use your hands to bring the dough together and form a disk approximately 8" in diameter and ¾" thick. Cut into 8 slices and transfer them individually to the parchment-lined baking sheet.
Brush the tops of the scones with milk to help with browning and bake for 16-17 minutes until firm. Once removed from the oven, immediately brush the tops with butter and sprinkle with some cut chives. Optional but recommended.
Allow to cool for at least 10 minutes before enjoying, or allow to cool completely. Enjoy!