Step 1: In a large skillet or wok, heat 1 tablespoon of sesame oil over medium-high heat. Add the ground pork and cook, breaking it apart with a spoon, until it is no longer pink and is nicely browned. Drain off any excess grease and set aside in a large mixing bowl.
Step 2: To the same skillet, add the remaining 1 tablespoon of sesame oil. Add the minced garlic and grated ginger, cooking for about 30 seconds until fragrant. Be careful not to burn the garlic.
Step 3: Add the shredded cabbage and carrots to the skillet. Sauté for 5-7 minutes, stirring occasionally, until the vegetables have softened slightly but still retain a bit of their crunch.
Step 4: Add the chopped green onions, soy sauce, oyster sauce (if using), rice vinegar, and a pinch of black pepper to the vegetables. Stir well to combine and cook for another 2-3 minutes, allowing the flavors to meld. Remove from heat.
Step 5: Combine the cooked vegetable mixture with the browned pork in the large mixing bowl. Stir thoroughly to ensure everything is evenly distributed. Let the filling cool completely before wrapping.
Step 6: Prepare your workstation: have your cooled filling, egg roll wrappers, and a small bowl with a beaten egg (the egg wash) ready. Keep the unused wrappers covered with a damp paper towel to prevent drying.
Step 7: Lay one egg roll wrapper on a clean, flat surface with a corner pointing towards you (like a diamond). Place about 2-3 tablespoons of the cooled filling diagonally across the center of the wrapper, forming a log shape.
Step 8: Fold the bottom corner of the wrapper over the filling, tucking it in tightly. Then, fold in the side corners towards the center.
Step 9: Starting from the bottom, roll the wrapper tightly upwards, forming a cylinder. Before you reach the top corner, brush the top corner with a little egg wash.
Step 10: Continue rolling until completely sealed. Place the finished egg roll, seam-side down, on a baking sheet lined with parchment paper. Repeat with the remaining filling and wrappers.
Step 11: In a large, heavy-bottomed pot or Dutch oven, pour enough vegetable oil to reach a depth of about 2-3 inches. Heat the oil over medium-high heat to 350-375°F (175-190°C). Use a candy thermometer for accuracy.
Step 12: Carefully place 3-4 egg rolls into the hot oil, ensuring not to overcrowd the pot. Fry for 4-6 minutes, turning occasionally, until they are golden brown and crispy on all sides.
Step 13: Using a slotted spoon or tongs, carefully remove the fried egg rolls from the oil and transfer them to a wire rack set over a baking sheet lined with paper towels.
Step 14: Repeat the frying process with the remaining egg rolls. Serve immediately with your favorite dipping sauce.