Grate cold butter then place into freezer while preparing the rest of the ingredients so it stays very cold.
In a large mixing bowl, add dry ingredients and whisk together.
Add in cold butter and mix using fingers (or a pastry cutter) to coat the butter evenly within the gluten-free flour mixture.
Add Greek yogurt, egg, grated cheese, and chives to a separate small bowl and mix using a spatula, then pour into the dry ingredients. Mix well until evenly combined and dough starts to form.
Using clean, wet hands form dough into a ball and flatten into a disc onto a clean work surface. About 7 inches in diameter.
Cover tightly in plastic wrap and place in refrigerator for 30 minutes.
After 30 minutes of chilling in refrigerator, preheat oven to 500°F and place the disc into the freezer to chill another 15 minutes. Line a baking sheet with parchment paper.
After 15 minutes of chilling in freezer, cut the dough in half, then cut each half into equal thirds. 6 scones altogether. Place on prepared baking sheet, then into the preheated oven and immediately turn oven temperature down to 425°F.
Bake for 12-14 minutes until scones are golden.
After baking, transfer scones onto a wire rack and allow to cool for 20 minutes.
Melt 2 tbsp butter and if using, add ¼ tsp garlic powder to melted butter. Brush onto cooled scones and serve.