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Step 1
Cut the legs from the chickens. Pull off the skin that covers the breasts, then cut the breasts from the carcasses. Cover and refrigerate 2 breasts for the ramen. Cover and refrigerate or freeze the remaining 2 breasts and the legs for another use.
Step 2
Bring a medium pot of water to a boil. Add the chicken carcasses one at a time and cook for 30 seconds to blanch and clean the chicken. Transfer the carcass to a very large pot, arranging in a single layer in the center. Strain any scum off the top of the water and bring back to a boil. Add the chicken feet and cook for 60 seconds. Transfer the chicken feet to the pot with the carcasses, arranging them around the carcasses.
Step 3
Place the onion quarters down the center on top of the carcasses. Add the water. Bring to a simmer uncovered over medium-high heat watching closely and reducing heat to maintain a simmer, skimming off any scum as soon as it forms at the top of the stock. Do not let it come to a boil. Continue to simmer, skimming the stock as needed and maintaining the heat to ensure it simmers and does not boil. Try not to agitate the stock to keep it clear. The stock will start out with a greyish color but will turn golden as it simmers. When you start to notice the color of the stock changing, after about 1 hour, turn the heat to low and cover the pot. Simmer until the stock is golden yellow, about 3 more hours.
Step 4
Meanwhile, turn a gas burner on to medium to medium-high. Hold on to the dark green part of the leek with your hand or tongs with the white part of the leek over the flame and cook, turning occasionally, until the white outer layer is charred all over. Alternatively, this can be done under the broiler. Cut off the dark green part of the leek and store the charred leek airtight until cooled.
Step 5
Peel off the outer charred layer from the leek and add to the stock. Add the cabbage, mushrooms, katsuobushi, if using, Parmesan rind, ginger, and rock sugar. Simmer the stock, covered with the lid slightly ajar, until the stock is golden and aromatic, 2 to 4 more hours.
Step 6
In a small pot, add the chicken breasts and enough chicken stock to cover. Bring to barely a simmer over medium-low and poach the chicken until just cooked through, 10 to 20 minutes. Cut the chicken into 3/4 inch cubes. Strain the stock and return to the large pot of stock.
Step 7
Bring a medium pot of water to a boil. Add the bean sprouts to the boiling water and cook for 30 seconds. Using a handheld strainer, transfer the sprouts to a small bowl. Add the spinach to the boiling water and cook just to wilt, about 1 minute. Using a hand-held strainer, transfer the spinach to a work surface. Let the spinach cool, then roll into a log shape about 6-inches long. Cut crosswise into 4 equal portions and reserve for the topping. Fill the pot with fresh water and bring to a boil for the noodles.
Step 8
In a mortar and pestle, coarsely grind the Sichuan peppercorns, cumin, star anise, and cloves. In a small skillet, heat the chicken fat over medium heat. Add the onion and cook, stirring often, until deep golden brown, about 5 minutes. Spoon 2 tablespoons of the onion oil into a large pot and heat it until it shimmers. Add the garlic to the pot and stir fry until translucent, just a few seconds. Add the chile and cook, stirring often, until aromatic, about 2 minutes. Add most of the spice mixture (save a little for garnishing) and stir until fragrant and the garlic begins to turn golden brown, about a minute. Add the toban djan and black bean paste and stir until fragrant and fruity, about 1 minute. Add the sugar and stir until it dissolves, just a minute. Add the Shaoxing and cook until the smell of the alcohol disappears. Stir in 1/4 cup of the chile oil and soy sauce. Add the tofu and poached chicken, and gently fold the mixture to coat while still on high heat.
Step 9
Stir the stock into the pot and cook until heated through, 2 to 3 minutes. In a small bowl, stir the cornstarch and water until smooth. Stir in the cornstarch slurry by the teaspoonful or so until the desired consistency forms.
Step 10
Add the noodles to the boiling water and cook until tender but still firm to the bite, about 1 minute. Drain the noodles.
Step 11
Using a slotted spoon, transfer the tofu and chicken to a medium bowl. Divide the mapo tofu broth among four bowls. Add the noodles to the bowls, folding over to create one flowing direction (pick up, fold forward, then fold backwards) Top with the chicken and tofu, dividing equally. Garnish with the bean sprouts, spinach, and scallions. Top with a few pinches of the remaining spice blend and a small spoonful of the chile oil.