Cover a baking sheet with a piece of parchment paper, and set aside.
Place the cheddar cheese and chiles in a small bowl, and toss to combine; set mixture aside.
In a small bowl, lightly beat 3 eggs and the cream, and set aside.
Using an electric mixer fitted with the paddle attachment, combine flour, baking powder, chile powder, and salt. Add butter; mix on low speed until the butter is in pea-size pieces, 1 to 2 minutes. Add egg and cream mixture; mix on low speed until just blended. Add cheese and chile mixture; mix until just combined.
Transfer dough to a well-floured surface, and pat into a 9-inch circle. Using a sharp knife dipped in flour, cut circle into 8 to 12 wedges. Transfer wedges with a spatula to prepared baking sheet; brush tops with egg wash.
Place in oven; bake, until outside is crusty and inside is cooked through, 15 to 20 minutes. Transfer to a wire rack to cool.
Notes
Chose chiles according to your tolerance for spice. I ended up making a second batch for my kids and instead of using the spicy chile in my freezer I used a can of Old El Paso chopped green chiles for a milder and child-friendly version. My children really enjoyed them.