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1
Set the oven to 180 °C. If making the chorizo version, place crumbled chorizo in a dry skillet over medium heat and cook, breaking it up, until the fat has rendered and the meat is cooked through. Drain away all rendered fat. Set the meat aside. The chorizo must be entirely free of pooled fat before it meets the cheese.
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2
For the rajas variation: roast the poblano chillies directly over a flame or under the broiler, turning, until the skin is uniformly charred and blistered. Place in a covered bowl for 10 minutes, then peel, seed, and cut into strips roughly 1 cm wide. Combine with corn kernels.
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3
Layer the quesillo strips and grated Chihuahua cheese into a small cazuela or cast-iron skillet. Add the splash of beer or white wine. The cheeses must fill the vessel generously — they will contract as they melt.
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4
Place the cazuela in the oven and melt the cheese slowly over low, even heat. This is the step on which the dish lives or dies: high heat will render the fats out before the proteins relax, leaving a rubbery, greasy result. The cheese is ready when it is fully molten, glossy, and moves in a single mass when the pan is tilted — not when it bubbles violently.
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5
Scatter the drained chorizo evenly over the surface (or arrange the rajas and corn, then spoon over the crema for the rajas version). Return the cazuela to the broiler for 60 seconds until the top is lightly bubbled and spotted gold.
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6
Carry the cazuela directly to the table in its cooking vessel. The queso fundido must be served at once: it sets firm as it cools. Serve with warm corn tortillas on the side for scooping.