Cut veal into 24 four-ounces slices. Pound slices into a square shape, _-inch thick. Cut green onions into pieces as long as the pounded veal slices.
Place 1 green onion at end of 1 veal slice; roll up jelly roll style, enclosing onion. Tie roll at 1½-inch intervals. Repeat with remaining veal and onions. Refrigerate, covered.
Lightly brown 2 veal rolls under the broiler. Finish cooking rolls in oven.
Sauté 2 ounces shiitake mushrooms, 1 ounce shallot and 1 teaspoon garlic in 1 tablespoon oil until tender. Deglaze pan with 1 ounce wine. Stir in 1 ounce each consommé and teriyaki sauce. Season with pepper. Add 2 ounces enoki mushrooms; cook and toss until firm-tender. Remove from heat; whisk 1 tablespoon butter into sauce until blended. Keep warm.
Cut veal rolls crosswise into thin slices. Arrange slices in a circle on plate. Pour mushroom sauce into center of circle.