Heat the vegetable oil in a large skillet over medium high heat.
When hot add the cabbage and shredded carrots to the skillet and cook, stirring often, until the cabbage and carrots soften, 7-10 minutes.
Add the green onions, soy sauce, sugar, toasted sesame oil, five spice powder, salt, and shrimp to the cabbage mix. Remove from the heat and stir everything together.
Place an egg roll wrapper on a flat surface with a corner facing up so that it is in a diamond shape.
Place approximately 3 ounces of the cabbage filling just below the centerline of the wrapper.
Lift the bottom corner and fold it up and over the fling tucking it underneath. Use your fingers to gently press down on each side of the filling to make sure it is packed in and tightly sealed.
Fold the side corners into the middle. Now it makes a sort of envelope shape.
Dip a brush in the beaten egg and lightly brush the egg over the top corner of the wrapper. This will make it stick when you roll the wrapper up.
Roll the egg roll up so that the remaining corner wraps around the egg roll sealing it all together.
Repeat steps until all of the filling is used.
Preheat the air fryer to 400 degrees F for 3 minutes.
Once the rolls are ready lightly brush each roll with a very thin layer of peanut oil. If you have an oil sprayer you can fill it with peanut oil and spray the eggrolls. Make sure to use a very light layer of oil on each side.
Place the rolls in the pre-heated fryer basket so that there is a bit of room between each.
Cook at 400 degrees F for 5 minutes then stop and flip over and continue to cook for 5 minutes more.