Prepare the Shrimp: Gently wash the cleaned shrimp in cold water, then use paper towels to blot them dry. Dredge the shrimp in all-purpose flour until thoroughly coated, then shake off any extra flour and set them aside.
Fry the Shrimp: Heat ¼ cup of vegetable oil in a large skillet or wok over medium-high heat. Add the shrimp in batches and fry until they turn golden and crispy, about 2-3 minutes per side. Remove the shrimp and set aside on a paper towel-lined plate to drain excess oil.
Toast the Szechuan Peppercorns: In the same skillet, add the Szechuan peppercorns and toast them over medium heat until fragrant, about 1-2 minutes. Remove and grind them coarsely with a mortar and pestle, then set aside.
Sauté the Aromatics: Add 2 tablespoons of vegetable oil to the skillet and heat over medium-high heat. Incorporate the sliced ginger into the pan and sauté for 1-2 minutes until it becomes aromatic. Toss in the dried red chilies and chopped white parts of the green onions. Stir-fry for another 1-2 minutes, being careful not to burn the chilies.
Prepare the Sauce: In a small bowl, mix together the soy sauce, sesame oil, Shaoxing wine, and sugar. Stir until the sugar dissolves completely.
Combine Everything: Return the fried shrimp to the skillet and pour the sauce over them. Add the ground Szechuan peppercorns and the green parts of the onions. Stir-fry everything together for 2-3 minutes, ensuring the shrimp are evenly coated with the sauce and the flavors are well combined.
Serve: Transfer the Szechuan Chili Shrimp to a serving dish and garnish with additional green onions if desired. Serve hot with steamed white rice or as an appetizer. Enjoy the spicy, numbing, and flavorful shrimp!