Preheat oven to 375°F. Line a rimmed baking sheet with parchment paper then spray with cooking spray.
Place a sauté pan over medium heat. Once pan is hot, add sesame oil and scallions, then sauté for 3 minutes. Add garlic and sauté 1 minute more. Add cabbage, carrots, mushrooms, salt and pepper. Sauté for 10 minutes more or until cabbage is wilted and reduced in size by half. Add teriyaki marinade & sauce to the pan and cook 2 minutes more. Set aside to cool.
Place 1 egg roll wrapper on a cutting board or countertop. Place 3 tablespoons of filling in center. Roll pointed edge over filling. Fold the right and left side toward the center of eggrolls and roll tightly. Place seam side down on the prepared baking sheet. Repeat with remaining egg roll wrappers.