Heat the chicken bone broth, two cloves garlic, shallot and ginger. Add salt, the amount depending on how salty the broth is.
Bring to a simmer and drop in the chicken breast fillets. Poach the chicken for ten minutes then remove from the broth. Cool the chicken.
Make the sauce. With a mortar and pestle, pound the Sichuan peppercorns until powdery.
Peel the remaining two cloves of garlic and add to the Sichuan peppercorns. Sprinkle in the sugar. Pound until pasty.
Add the sesame paste slowly with constant stirring.
Add the soy sauce, black vinegar and chili oil with the bits of chili. Stir until smooth. Taste and make the necessary adjustments in accordance with your taste.
Pull the chicken breasts apart into rather chunky shreds. Toss with the prepared sauce.
Line a plate with shredded lettuce. Arrange the chicken on top. Sprinkle with toasted sesame seeds and sliced scallions. Drizzle with more chili oil and serve the Sichuan bang bang chicken.