Preheat the oven to 450°F (232°C).

In a large bowl, combine the Queso Oaxaca, Pepper Jack, and Mozzarella cheeses and toss lightly to mix.

Place an oven-proof 10-inch skillet over medium heat. Add the chorizo and cook, stirring occasionally, until crisp and fully cooked, about 8–10 minutes. Using a slotted spoon, transfer the cooked chorizo to a large bowl, leaving the pan drippings in the skillet.

Add the chopped onions to the hot skillet and cook over medium heat until soft and translucent, about 3–4 minutes. Add the minced garlic and cook, stirring, for about 30 seconds.

Scrape the cooked onions and garlic into the bowl with the chorizo and stir to combine.

Scoop out and set aside 1/4 cup of the chorizo-onion-garlic mixture for topping. To the remaining chorizo mixture in the bowl, add the 4-oz can of diced green chilies (drained if desired) and stir until evenly distributed.

Sprinkle half of the mixed cheeses (about 1.5 cups) evenly across the bottom of the same 10-inch skillet.

Spread the chorizo and chili mixture over the cheese layer in the skillet.

Top with the remaining half of the mixed cheeses, spreading them evenly over the chorizo.

Bake in the preheated oven until the cheese is fully melted and bubbly, about 20 minutes.

Remove the skillet from the oven. Sprinkle the reserved 1/4 cup chorizo-onion mixture on top, then garnish with chopped cilantro and sliced green onions. Serve immediately.