Heat vegetable oil in a tabletop fryer or Dutch oven to 350 degrees F.
Bring a large pot of water to a boil.
In a medium bowl, combine the cornstarch, ground Sichuan peppercorns, five-spice powder, sugar and 1 teaspoon salt. Toss the prawns in the cornstarch mixture, then gently place in the fryer. Cook until golden brown and cooked through, about 3 minutes. Remove to a paper towel-lined plate and season with salt.
In a wide, shallow pot set over medium-high heat, add a few turns of the pan of oil. Add the reserved shrimp heads and shells and saute a few minutes, until pink and fragrant. Add the whole Sichuan peppercorns, fennel seeds, star anise, cinnamon sticks and cloves. Toast for a minute or two. Add the garlic, leeks and ginger and cook for a few minutes. Add the chicken stock, Shaoxing wine and shoyu and bring to a simmer. Let reduce by about half, then strain through a fine-mesh strainer and reserve.
Place a small nonstick skillet over medium-high heat and add a turn of the pan of oil. Add the egg, letting it run around the pan, gently picking up the cooked part and letting it continue to run. Remove from the pan, roll and thinly slice. Set aside.
Place a large skillet over high heat and add a few turns of the pan of oil. Quickly saute the carrots, scallions, cabbage and mushrooms for a minute or two.
As soon as you start cooking the vegetables, drop the noodles in the boiling water and let cook for a couple minutes. Remove from the pot and add straight to the pan of vegetables. Add some of the reduced shrimp head liquid and toss to combine.
Transfer to a plate or platter and top with the sliced egg and cooked shrimp.