Place stock in a medium saucepan, reserving 1/4 cup, and bring to a simmer. Meanwhile, place remaining 1/4 cup stock and the rehydrated ancho chiles in a blender and puree until combined. Add pureed anchos, porcini, and hominy and cook for 10 minutes. Add the chicken and cilantro and cook for 5 minutes. Season with salt and pepper, to taste.
Ladle soup into bowls and top with cheese and some fried tortillas.
Preheat oven to 450 degrees F.
Combine chicken bones, onions, celery, and carrots in a large roasting pan; toss with oil and season lightly with salt and pepper. Roast until the bones and vegetables are a rich golden brown, about 30 to 40 minutes.
Transfer the bones and vegetables to a large stockpot, add 12 cups cold water, and the remaining ingredients and bring to a boil over high heat. Reduce the heat to medium and simmer for 4 hours, skimming the scum that rises to the top with a ladle every 20 minutes. Remove from the heat and strain through a mesh strainer into a clean pot. Place back on the stove over high heat and cook until reduced by half. Use immediately or let cool to room temperature, cover, and refrigerate or freeze until ready to use.
Heat oil in a high sided large saute pan until it reaches 350 degrees F. Add the tortillas in 2 batches and cook until just crisp. Transfer to a plate lined with paper towels and season with salt immediately.