Preheat oven to 375°F.
Whisk together flour, baking powder, salt, and sugar.
Using a pastry blender or your fingers, work the butter into the flour mixture until it’s like coarse crumbs.
Add both cheeses into the flour and stir well to combine.
Add the green chile and stir well, using your fingers if necessary, to get the green chile well distributed throughout the flour mixture.
Stir in the cream. Add more if necessary, in small increments, until it’s just moistened.
Turn out onto a floured surface. Bring the dough together and pat it out. Fold it on itself and roll it out 3 times so that you create some layers. Do this gently.
Form into a disc and roll out into a circle of about 1-in thickness.
Cut into 8 wedges. Place on a baking sheet with parchment paper.
Brush the tops and sides of the scones with the whisked egg.
Bake for 18–20 minutes, or until tops and bottoms are golden brown.