1. Preheat oven to 350 degrees F. Spray a baking sheet with cooking spray. Dissolve 1 tablespoon of the cornstarch into 1/4 cup water and set aside.
2. Lightly spray a large skillet with cooking spray and heat over low. Cook cabbage, carrots, mushrooms, water chestnuts, and ginger in the pan until cabbage is just wilting (5-7 minutes). Stir in cornstarch mixture and soy sauce.
3. Cook until the sauce thickens (2-3 minutes). Stir in the green onions and remove pan from heat.
4. Dissolve the remaining tablespoon of cornstarch in remaining 1/4 cup water. Brush onto egg-roll wrappers, fill with vegetables, and wrap. Place rolls on the prepared baking sheet and bake until brown (15-20 minutes).