In a large mixing bowl, whisk together the gluten-free flour, sugar, baking powder and salt.
Grate the frozen butter using a box grater. Add it to the flour mixture and combine with a pastry cutter, two forks, or your fingers until the mixture comes together in pea-sized crumbs.
Stir in the mix-ins to the flour mixture until evenly distributed. In a separate bowl, whisk together the sour cream and egg until combined.
Using a rubber spatula, stir the sour cream mixture into the flour mixture until no dry bits of flour remain. Fold in the cheddar cheese.
Spread out a large piece of plastic wrap. Using wet hands, transfer the dough to the parchment paper. Clean and wet your hands again then pat the dough to form a 6-inch round that is 1-inch thick. Wrap the dough tightly in plastic and refrigerate for 30 minutes. (Do not refrigerate longer than 30 minutes.)
Preheat the oven to 500F. Line a baking sheet with a silicone mat or parchment paper.
After 30 minutes take the dough out of the fridge. Spray a sharp knife with vegetable oil and cut the dough into 6 equal wedges. Arrange the scones on the prepared baking sheet.
Lower the oven temperature to 425F and bake the scones for 12-14 minutes until golden brown. (You want the oven temperature to be hot to start so the scones turn golden brown as they cook through.)
Transfer the scones to a cooling rack and let cool for 20 minutes before serving.
Whisk the garlic chive butter ingredients together. After cooling for 20 minutes, brush the tops of each scone with the butter.