Set an oven rack in the middle of the oven, about 6" from your broiler. Turn broiler on high. Heat the olive oil in a 9" nonstick skillet over medium heat. Add the green chiles; sauté until any excess moisture is cooked off, about 2 minutes.
Meanwhile, crack the egg into a medium-sized mixing bowl. Add the whipping cream, salt, and pepper. Whisk vigorously to blend and incorporate plenty of air into the mixture.
Reduce heat to low and add the egg mixture to the skillet. Use a silicone spatula to quickly redistribute the chiles throughout the egg mixture (it doesn't have to be uniform). As the egg mixture begins to set up (about 3 minutes), run the spatula around the outer edge of the egg mixture, then tilt the pan all the way around to let some of the loose egg mixture on top to run all around the sides. Meanwhile, start warming the tortilla (see Recipe Note #1).
Turn off the burner. Sprinkle cheese over the top of the frittata and transfer skillet to the oven, leaving the door cracked so you can keep tabs on the frittata. Turn the skillet 1/2 turn during the broil (after 1–2 minutes). The egg mixture will firm up and become slightly puffy, but don't let the frittata brown at all. Remove from the oven and turn off broiler.
Use the silicone spatula to gently loosen the egg mixture from the pan. Place the tortilla on a plate and invert the skillet over the top to release the frittata. Fold up the bottom ~1/4 of the tortilla over the bottom of the frittata mixture, then roll up from the left or right side. Enjoy!