Preheat oven to 350 degrees F. In an 8 inch oven-safe skillet, drizzle the vegetable oil over medium heat. Add the onion and cook, stirring occasionally, until softened. Stir in the garlic and cook until just fragrant, 30 seconds to 1 minute.
If in sausage form, remove the chorizo from the casing and crumble into the pan. Cook, stirring often and breaking apart the pieces, until heated through, about 7 minutes.
Drain excess fat from the skillet and remove a couple of tablespoons of the chorizo to a plate to save for garnish. Spread the chorizo left in the pan in a thin layer and evenly top with the shredded cheese. Transfer the pan to the preheated oven. Bake just until the cheese is melted and starting to bubble, 10-12 minutes.
Sprinkle with cilantro and reserved chorizo. Serve hot with the salsa and tortillas/tortilla chips.