Preheat the oven to 400 degrees Fahrenheit.
Finely chop 3 tbsp of fresh chives. Set aside.
Measure 2 cups flour into a large mixing bowl. Add the baking powder, sugar, and salt and whisk together. Set aside.
Grate the frozen butter and add it into the dry ingredients. Quickly combine with your hands. If the butter starts to melt, pop the bowl into the fridge for a few minutes.
Pour in the heavy cream and stir to combine using a wooden spoon.
Lightly beat the egg and add to the dough. Stir until completely combined.
Add in the finely shredded cheddar and the chopped chives. Stir to combine. Some of the flour may still be unmixed.
Test the dough by seeing if a small portion pulled off will form a ball when squeezed. If it is still very crumbly add 1 tbsp of heavy cream, stir, and try again. If it remains very dry, add up to one additional tablespoon of cream. There will be a few crumbs that do not mix in, but the majority should form a cohesive dough.
Tear off a sheet of parchment paper large enough to line the baking sheet. Place the paper on your work surface.
Pour the dough onto the parchment paper and knead until all of the dough comes together, a out 30 seconds to 1 minute. Discard any loose crumbs that remain.
Pat the dough into a square shape and roll out to form an 8 inch square, about 1/2 inch thick.
Place the parchment paper and the dough onto the baking pan.
Use a bench scraper or large sharp knife to cut the dough into 12 evenly sized squares. Place scones about 1 inch apart to leave room for spreading.
Add 2 tbsp of heavy cream to a mug or small bowl.
Use a pastry brush to evenly brush heavy cream over the top of each scone.
Lightly sprinkle coarse sea salt on top of the scones. This is optional but adds taste and a great crunch.
Bake until golden brown, about 18-20 minutes.