Begin by heating a skillet over medium heat. Add the chorizo, breaking it apart with a spatula as it cooks. Sauté until it's browned and cooked through, about 5-7 minutes. Drain excess fat if necessary.
Add the chopped onions to the skillet with the chorizo. Cook for about 3 minutes until the onions are translucent. Stir in the minced garlic and cook for an additional minute, allowing the aroma to fill your kitchen.
Stir in the can of diced green chilies, mixing well. Let the mixture simmer for 2-3 minutes to allow the flavors to meld together.
Reduce the heat to low and start adding the shredded cheeses to the skillet. Begin with the Queso Oaxaca, followed by the Pepper Jack, and finally the mozzarella. Stir continuously until the cheeses are fully melted and combined, creating a luscious, gooey mixture.
Once everything is well combined, transfer the cheesy chorizo mixture into an oven-safe dish, spreading it evenly.
Preheat your oven to 375°F (190°C). Place the dish in the oven and bake for about 10-15 minutes, or until the top is bubbly and slightly golden.
Remove the dish from the oven and garnish with chopped cilantro and sliced green onions. Serve immediately with tortilla chips, warm bread, or fresh veggies for dipping.