Add carrots and green onions to skillet and sauté for 2 minutes.
While cooking, whisk together soy sauce, sugar, and broth.
Stir soy sauce mixture, cabbage, and shrimp into the vegetables in skillet and cook 5 minutes.
Remove skillet from heat and allow to cool for about 15 minutes. Afterward, strain the liquid through a strainer.
Preheat Bravo to 390°F. Set to “Air Fry” and set Cooking Rack in position.
Place the egg roll wrappers on a work surface. Top each with 3 T veggie/shrimp mixture.
Brush some egg on the edges of each wrapper. Roll up the wrappers, folding over the sides so filling is contained.
Spray Air Fry Basket with cooking spray. Brush egg on the outsides of each egg roll before adding to the Air Fry Basket. Carefully add 3-4 egg rolls at a time to Basket. Brush tops of egg rolls with egg. Air fry 8-9 minutes, or until brown and crispy on the outside.
Serve immediately with sweet and sour sauce, hot mustard sauce, or both.