Preheat oven to 375 degrees. Using small knife, pierce potatoes in several places. Place potatoes on small baking sheet. Bake until tender when pierced with skewer, about 1 hour. Cool slightly.
Bring half and half to simmer in heavy small saucepan. Scrape potatoes from skin into large bowl. Using ricer, food mill or potato masher, mash potatoes. Mix in half and half. Add butter; stir vigorously until butter melts and potatoes are smooth. Stir in ⅔ of cheese and 2 Tbsp chopped parsley or chives. Season with salt and pepper. Transfer potatoes to 11x7x2-inch glass baking dish. Sprinkle with remaining cheese. (Can be prepared 2 hours ahead. Cover and let stand at room temperature.)
Preheat oven to 425 degrees. Bake potatoes until heated through and cheese melts, about 15 to 20 minutes. Sprinkle with remaining parsley or chives after baking.
Makes 6 servings.