Marinate chicken cubes in 1 tablespoon Shaoxing wine and ½ teaspoon salt while you prep the vegetables.
Add Sichuan pepper, cumin seeds and fennel seeds to dry skillet and toast until fragrant. Allow to cool slightly, then grind coarsely in a spice grinder or mortar & pestle. Add chili flakes and salt and mix well.
Heat wok on high until almost smoking. Add enough peanut or canola oil to deep-fry the chicken, and heat to about 375°F. Fry chicken until golden brown, then remove to paper-towel-lined plate and reserve.
Bring a large pot of water to a boil, and add vegetables: first add the potato slices for about 30 seconds, then the pre-soaked tofu skin, followed by the broccolini, celery and red bell slices. Return to a boil and cook only until the vegetables are just cooked through and still crisp, about 2 minutes. Drain in a colander and rinse with cold water to stop cooking process.
Clean wok and return to high heat until almost smoking. Heat 3 tablespoons oil until hot, then add onions. Stir-fry until softened, then add green chili peppers, garlic, ginger and dried red chilies. Stir-fry vigorously so that nothing browns or burns.
Shove aromatics to the sides of the wok and make a well in the center. Add 2 tablespoons oil and then the spice mixture. Cook briefly, then add the chili bean paste and cook briefly, until fragrant.
Add the parboiled vegetables to the wok and mix well with the aromatics and seasonings. Drizzle the Shaoxing wine and soy sauce around the edges of the wok. Add the chicken and the scallions and stir-fry briefly, mixing well with other ingredients.
If wok and ingredients get too dry at any point during the stir-fry process, add chicken broth just to moisten. When all ingredients are mixed and cooked through, plate and garnish with sesame seeds.