Preheat oven to 350°F. In a small bowl, toss together cheese and the 2 tablespoons snipped herbs; set aside. Coat a 3-quart oval or rectangular baking dish with oil.
In the prepared baking dish, layer half of the sliced vegetables and 1 1/2 cups of the cheese mixture; sprinkle lightly with salt and pepper. Top with remaining sliced vegetables, reserving the remaining 1 1/2 cups cheese mixture.
Bake, covered, for 35 minutes. Uncover. Bake for 10 to 15 minutes more or until vegetables are nearly tender. Sprinkle with the remaining cheese mixture.
Increase oven temperature to 400°F. Bake, uncovered, about 15 minutes or until cheese melts and starts to brown. Remove from oven. Sprinkle with additional fresh herbs. Let stand for 10 minutes before serving.
Slice the russet potatoes just before layering to prevent them from discoloring.
Shred cheese. Place in a storage container; cover and chill up to 24 hours.