Despite its forty cloves of garlic, this soup is satisfyingly mellow.
Preheat oven to 400 degrees. Toss whole garlic cloves, potato, onion, sage, 1 tablespoon oil, 1 teaspoon salt, and a pinch of pepper in a large ovenproof skillet. Cover, and transfer to oven. Roast, stirring occasionally, 30 minutes.
Meanwhile, make the garnish: Put remaining 1 1/2 teaspoons oil and the sliced garlic into a small skillet. Cook over low heat, swirling skillet occasionally, until garlic is browned but not burned, about 20 minutes. Using a slotted spoon, transfer garlic slices to paper towels to drain.
Remove skillet from oven, and stir in 1/3 cup water. Cover, and return to oven; roast until potato is deep golden brown and garlic and onion are very soft, about 20 minutes. Transfer garlic cloves to a plate, and let cool slightly. Squeeze garlic from skins into skillet; discard skins.
Heat skillet over medium-high heat. Add sherry, and cook, stirring to scrape up browned bits, 1 minute. Add stock and 1/2 cup water, and bring to a simmer. Remove from heat, and let cool slightly.
Puree vegetable mixture in a blender in batches. Press through a fine sieve into a medium saucepan. Heat over low heat; stir in lemon juice, remaining 1/2 teaspoon salt, and 1/4 teaspoon pepper.
Divide soup among 6 bowls, and garnish with toasted baguette slices, fried garlic, and chives.