Whisk together the flour, sugar, baking powder and salt in a large bowl. Add in the cubed butter and cut in with a pastry cutter until the size of peas.
Mix the two eggs and cream together in a small bowl and add to the flour mixture. Don't overmix.
Stir in the cheddar and chives and mix until just incorporated.
Turn the dough onto a well floured cool or cold surface if possible. Knead about 4 times gently and work into a round about 3/4" to an 1" thick. Cut out into 2 1/2" rounds. Place on lightly greased cookie sheets.
You can rework the dough and make more but they won't turn out as great as the first ones do but still very good.
Whisk the final egg in a small bowl and brush on top of the scones. Let them rest for 10 min. Preheat oven to 375F.
Bake for 18-20 min. or until golden brown.
Nutrition calculation is an estimation only. If you need nutritional calculations for medical reasons, please use a source that you trust.