Preheat oven to 375F. Lightly butter a 9-inch diameter circle in the center of a baking sheet.
In a large bowl, stir together the flour, sugar, baking powder, salt, chili powder, cumin and pepper. Cut the butter into 1/2-inch cubes and distribute them over the flour mixture. With a pastry blender or two knives used scissors fashion, cut in the butter until the mixture resembles coarse crumbs. In a small bowl, stir together the egg, milk, and chilies. Add the egg mixture to the flour mixture and stir to combine. The dough will be sticky. With lightly floured hands, knead in the cheese until evenly distributed.
With lightly floured hands, pat the dough into an 8-inch diameter circle in the center of the prepared baking sheet. Brush the egg mixture over the top and sides of the dough. With a serrated knife, cut into 8 wedges. Bake for 20 to 25 minutes, or until the top is lightly browned and a cake tester or toothpick inserted to the center of a scone comes out clean.
Remove the baking sheet to a wire rack and cool for 5 minutes. Using a spatula, transfer the scones to the wire rack to cool. Recut into wedges, if necessary. Serve warm, or cool completely and store in an airtight container in the refrigerator.