Cook chorizo in a large skillet over medium to medium high heat until cooked through, approximately 10-15 minutes.
Place the chorizo in the bottom of a small oven safe baking dish.
Sprinkle the Hatch green chiles over the chorizo sausage.
Mix the two cheeses together and sprinkle over the chorizo and peppers.
Bake the fundido until the cheese is completely melted, just starting to bubble, but not browned.
Remove from oven and garnish as desired (cilantro, lime, tomato, etc). Serve immediately with soft tortillas or chips.
You can often find Oaxaca cheese with other Mexican options in the refrigerated section, typically near fresh Italian options like pasta, and near yogurt or other dairy products.If you do not have or cannot find Oaxaca, simply use more Monterey Jack. Other great cheese options are pepperjack (which is Monterey Jack with some peppers in it) or even mozzarella. Anything stretchy that melts well is perfect. Control the heat level by using your heat preference of both the chorizo and Hatch chile peppers.