Heat your skillet over medium heat and add the ground turkey chorizo. Break it apart with your spatula and cook until browned and fully cooked through, about 7-8 minutes. Drain excess fat if necessary.
Add the chopped onions and minced garlic to the skillet with the chorizo. Sauté until the onions turn translucent and fragrant, about 4-5 minutes. Stir often to prevent burning.
Mix in the diced green chilies, distributing them evenly throughout the chorizo mixture. Cook for another 2 minutes to meld the flavors.
In a mixing bowl, combine the shredded Queso Oaxaca, Pepper Jack, and Mozzarella cheeses. Stir well to ensure an even blend that will melt consistently.
Reduce the heat to low and evenly sprinkle the cheese blend over the chorizo mixture in the skillet. Cover the skillet with a lid or aluminum foil and allow the cheese to melt slowly, about 5-7 minutes. You want it bubbly, melted, and stretchy.
Once the cheese is perfectly melted, sprinkle chopped fresh cilantro and sliced green onions over the top. Serve immediately with warm tortillas, crusty bread, or crunchy tortilla chips for dipping.