Heat grill to medium heat. Arrange mushrooms, zucchini and pepper pieces on grill. Brush with 1 tablespoon of oil; sprinkle with 1 1/2 teaspoons Italian seasoning. Cook over medium heat until softened, lightly browned and tender. Remove from grill. Cut zucchini slices in half. Reduce grill heat to medium-low. In small bowl, beat eggs, remaining 1 1/2 teaspoons Italian seasoning, salt and pepper, if desired, until thoroughly blended. In 10-inch nonstick omelet pan or skillet, heat butter until just hot enough to sizzle drop of water. Pour in egg mixture. As mixture begins to set, gently draw inverted pancake turner completely across bottom and sides of pan, forming large, soft curds. Continue until eggs are thickened and no visible liquid egg remains. Do not stir constantly. Arrange 1 mushroom, 2 pieces zucchini, and 1 piece of pepper on each of 4 half-slices of bread. Divide eggs evenly over vegetables. Top with remaining bread. Brush outside of bread lightly with remaining 1 tablespoon oil. Place panini on grill. Cook over medium-low heat until bread is toasted. Turn over carefully and repeat for second side. Serve immediately.