Step 1Toast the chiles in a small, dry skillet over medium heat until aromatic and very pliable, turning once or twice, about 5 minutes. Using scissors over a blender jar, cut them into thin strips. Add the garlic, onion, oregano and tomato puree and process on top speed until smooth. Strain through a fine sieve.
Step 2Bring the stock to a boil, remove from the heat and set aside.
Step 3Heat the oil in a large, deep skillet over medium heat. Add the fideo (break strands if in bundles). Cook, tossing, until golden brown. Using a slotted spoon, transfer to a colander set over a bowl. Pour off all but 2 tablespoons of the oil; return the skillet to the heat.
Step 4Add the chile mixture to the skillet and cook, stirring occasionally, until thickened, 5 minutes. Add stock and season with salt to taste. Bring to a boil, then add the fideo.
Step 5Lower the heat, cover the pan and cook until the pasta absorbs the liquid, about 15 minutes. It will still be slightly soupy.
Step 6While the fideo cooks, heat the oven to 400 degrees. Cook the chorizo in a small skillet over medium heat until just done, about 5 minutes. Drain on paper towels; keep warm.
Step 7When the fideo is cooked, place in a shallow 2-quart casserole. Sprinkle the chorizo over it. Toss the Jack and Cheddar cheeses together and sprinkle evenly over the top. Transfer to the oven and bake until the cheeses melt, 10 to 12 minutes. Serve at once, with crema or creme fraiche for garnish.