Preparation

Preheat oven to 375°F. Place cloves of garlic in the center of a 12-inch square of foil, drizzle with 1 teaspoon of the olive oil and toss to coat. Wrap the foil around the garlic and fold or crimp to seal. Roast until garlic is tender, about 1 hour. Cool slightly before using. (Garlic may be roasted ahead, and will keep in a resealable container for 5 days in the refrigerator.)
1. While the garlic is roasting, heat remaining olive oil with butter in a 3 3⁄4-quart saucepan over medium heat. Add the onion, carrot, and celery. Reduce heat to low, cover loosely and cook until vegetables are tender but not browned, 8 to 10 minutes. Stir in the stock, water, potatoes, herbes de Provence, and roasted garlic. Raise heat and bring to a boil. Reduce heat to medium low and simmer, loosely covered, until potatoes are tender, about 20 minutes. Turn off heat and let stand for 2 to 3 minutes.
2. Insert the hand blender into the saucepan, making sure the protective guard is submerged. Blend on Low, using an up-and-down motion, moving the blender slowly throughout the saucepan, until well combined, smooth, and no visible pieces of vegetables remain, about 1 to 1 1⁄2 minutes. Add half-and half, salt and pepper. Insert the hand blender and blend for an additional 15 to 20 seconds. Serve hot. Garnish with chopped fresh parsley if desired.