Heat vegetable oil in a large skillet over high heat. Add garlic and ginger and cook 1 minute.
Add green onions, carrot and red pepper. Sauté about 2 minutes.
Combine the broth, soy sauce and sugar in a cup. Add the cabbage, bean sprouts and the broth mixture to the skillet. Cook about 5 minutes until vegetables have softened and wilted. Continue to simmer until excess liquid has evaporated.
Add 1 Tbsp of the sesame oil and the cooked pork. Stir to mix and remove from heat.
Lay out the egg roll wrappers on a work surface. Start with a pointed corner facing you. Wet your fingers in water and wet the perimeter of the wrapper. Add about 3-4 Tbsps of the filling mixture, in a log shape, horizontally across the corner nearest you. You may need to set the filling slightly toward the center so it doesn't pass the outer edge of the wrapper. See Note 1.
Start with the corner nearest you and roll the wrapper away from you. Press the filling to condense it into a fairly firm log shape. After the first quarter roll tuck the two side corners into the center. Continue rolling so the side ends are close up and secured by the rest of the egg roll. The wet edge will make the wrapper hold together as rolled. Lay egg rolls out on a dry surface until they are all wrapped. You will get somewhere around 9 egg rolls depending on how much filling you use for each.
When ready to cook- preheat air fryer if your machine requires. Brush egg rolls with the remaining 1 Tbsp of sesame oil. Don't let them touch each other once you have brushed the oil or the wrapper may soften and tear. Distribute egg rolls over 2 trays in a single layer. On Roast setting (375°) book about 8 minutes. At halfway point switch the top and bottom trays and turn egg rolls over. The wrapper should be well browned and have bubbled up. Use your judgement to add time as required based on your machine's performance.
Serve with plum sauce or your favourite dipping sauce.
You can brush wrapped egg rolls with oil and freeze immediately, individually. To cook from frozen Roast at 375 ° about 10 minutes per side, switching trays and turning them over at the halfway mark. Wrapper should be well browned and bubbly.
Note 1: 3 Tbsps of filling makes a substantial egg roll when done. If you use less filling the wrapper will overlap substantially more and you will end up with more wrapper than filling, which makes a rather tough egg roll.