How to Make It
To make the salsa, light a grill or preheat a grill pan. Grill the tomatoes, tomatillos and onion slices over moderately high heat, turning, until charred in spots, 10 minutes.
In a medium saucepan, heat the 1 tablespoon of oil. Add the árbol chiles and garlic and cook over moderately low heat until lightly browned, about 2 minutes. Add the grilled tomatoes, tomatillos and onion and 1 1/2 cups of water. Simmer over moderately low heat until the onion is softened, about 30 minutes. Transfer to a blender and puree until smooth. Strain the salsa through a medium-mesh strainer; season with salt.
In a large saucepan, heat 2 inches of oil to 375°. Working in batches, fry the tortillas, turning occasionally, until golden and crisp. Using a slotted spoon, transfer the chips to a paper towel–lined plate to drain.
In a large bowl, toss the warm chips with half of the salsa. Transfer the chips in salsa to a platter and top with the cheese, cilantro and finely chopped onion. Serve right away, passing the remaining salsa at the table.