For the sausage patties: Mix the sausage and chorizo in a bowl until well combined. Form into 6 patties. Heat a skillet over medium-high heat. When hot, fry the patties in the dry skillet, flipping as needed, until cooked through, about 10 minutes.
For the eggs: Meanwhile, melt the butter in a large nonstick skillet over medium heat. Add the heavy cream, salt, pepper, eggs and green chiles to a pitcher. Whisk with a fork until well combined. Add the egg mix to the skillet and cook as you would an omelet, stirring, until the eggs begin to set, about 2 minutes. Allow the eggs to continue cooking until almost completely set, an additional 2 minutes. Using a spatula to help, flip the omelet in one motion. Let cook for 1 more minute, before sliding the whole thing onto a cutting board. Cut into 6 pieces.
For the sandwiches: Build the sandwiches by adding some of the chipotle mayonnaise to the bottoms of the English muffins. Place a sausage patty, slice of cheese and an egg portion onto the bottom half of each muffin. Spread a little more mayonnaise onto the top of the English muffins and top the sandwiches. Serve hot.