Step 1: Cook the Shrimp: In a large skillet, heat 1 tablespoon of vegetable oil over medium heat. Add the shrimp and cook until they turn pink and are fully cooked through, which should take about 3-4 minutes. Once the shrimp is done, remove it from the skillet and chop it into small pieces. Set it aside.
Step 2: Sauté Aromatics and Vegetables: Return the same skillet to medium heat, adding a touch more oil if needed. Sauté the minced garlic and grated ginger for 1-2 minutes until fragrant. Next, add the shredded cabbage, julienned carrots, and chopped green onions. Stir-fry for 3-4 minutes, until the vegetables soften slightly but still retain some crunch.
Step 3: Combine Filling Ingredients: Return the chopped shrimp to the skillet with the vegetables. Add the soy sauce, oyster sauce, and sesame oil. Stir everything together and cook for an additional 2-3 minutes, allowing the flavors to meld. Remove the mixture from the heat and let it cool slightly before proceeding.
Step 4: Assemble the Egg Rolls: Lay an egg roll wrapper flat on a clean surface, with one corner facing you (like a diamond). Place about 2 tablespoons of the shrimp and veggie mixture in the center. Brush the edges of the wrapper with the beaten egg to help seal. Fold the bottom corner over the filling, then fold in the side corners, and roll tightly from the bottom up, ensuring the filling is secure.
Step 5: Fry to Golden Perfection: In a large pan or deep fryer, heat vegetable oil to 350°F (175°C). Carefully place the assembled egg rolls into the hot oil, working in batches to avoid overcrowding. Fry for 3-4 minutes, or until golden brown and crispy on all sides, flipping as needed.
Step 6: Drain and Serve: Once fried, remove the egg rolls and place them on a plate lined with paper towels to drain any excess oil. Let them cool for a minute or two before serving with your favorite dipping sauce. Enjoy your deliciously crispy homemade treat!