Preheat broiler. Position top rack closest to the heating element. Lightly oil a full-size, rimmed baking sheet.
Make a slit lengthwise down the center each pepper, leaving the stem attached. Stuff each pepper with a slice of chorizo and cheese. Place on prepared baking sheet, leaving 1/2 space between each pepper for easy turning and even broiling. Broil peppers, turning frequently, until browned on all sides and skins are slightly blistered, about 3 to 4 minutes.