Preheat oven to 350 degrees and spray a 9x13 baking dish with non-stick cooking spray.
Heat a large skillet over medium heat. Add the chorizo (if it's in the casing, remove from casing first) and cook, breaking up the meat with the back of a spoon until cooked through, about 8 minutes. Remove from heat and set aside. (I don't drain mine, I like the added fat for flavor. But if your chorizo has an excessive amount of fat to it, drain off most of it, leaving 1-2 tbsp of the fat for flavor).
In a large bowl, whisk together the eggs, salt, pepper, and cream until very well combined and frothy. Set aside.
Spread the spiralized sweet potatoes across the bottom of the prepared baking dish. Next, spread the cooked chorizo (and the fat from the skillet) over the top of the spiralized sweet potato. Then, pour the egg mixture over the top. Gently shake the skillet so that everything is spread evenly. Sprinkle the cheese over the top (if using).
Place into the oven and cook until the eggs have just set, about 20 minutes.