In a large bowl, whisk together flour, baking powder, salt, and chives. Stir in grated cheese.
Add one cup of heavy cream into dry ingredients, gently mix together until cream has been completely absorbed. Add in remaining 1/4 cup heavy cream. Mix just until combined.
Lightly knead dough on a lightly floured surface. With lightly floured hands, form dough into a slightly flattened circle about 1 in thick. Using a bench scraper or knife, cut evenly into 6 large triangles. Separate and place on a non-stick baking sheet, making sure to leave space between them. Refrigerate until firm, about 1 hour.
Preheat oven to 400 degrees F. Brush scones with heavy cream. Bake for 16-20 minutes, rotating the pan halfway through baking, until golden brown and firmed. Remove from pan. Allow to cool before eating.
Recipe adapted from The Sono Baking Company Cookbook.