In a skillet, stir-fry the ginger and garlic in 1 tablespoon of oil about 30 seconds.
Add green onions, carrots, and red pepper and stir-fry over high heat for 2 minutes.
In a bowl, combine the water, soy sauce, and sugar.
Add the Napa cabbage and water mixture. Bring to a boil and simmer 5 minutes.
Add sesame oil, cool for 15 minutes, and strain.
Fold in the minced shrimp.
Fill and roll the egg roll wrappers, using 2 tablespoons of filling for each roll.
Place the wrapper with one corner of the diamond closest to you.
Place filling in the center of the wrapper.
Roll the corner closest to you over the filling.
Brush the top corner with water.
Fold in the sides of the wrapper and continue rolling the egg roll up until it is closed.
Press to seal.
In a skillet set over moderately high heat, heat the remaining oil and saute the egg rolls until golden brown on all sides.
Serve with dipping sauce.