Step 1

In a Dutch oven over medium heat melt butter. When foaming subsides, add leeks and cook until soft but not browned, 5 to 8 minutes. Add garlic and cook until fragrant, about 1 minute. Add garlic heads, broth, bay leaves, and salt; partially cover and bring to simmer over medium-high heat. Reduce heat and simmer until garlic is very tender when pierced with tip of knife, 30 to 40 minutes. Add potatoes and continue to simmer, partially covered, until potatoes are tender, 15 to 20 minutes.

Step 2

Discard bay leaves. Remove garlic heads; using tongs squeeze garlic heads at root end until cloves slip out of their skins. Using fork, mash garlic to smooth paste in bowl; set aside.

Step 3

Stir cream, thyme, and half of mashed garlic into soup; heat soup until hot, about 2 minutes. Taste soup and add remaining garlic paste to taste. Using an immersion blender, process soup until creamy, with some potato chunks remaining. Alternatively, transfer 1 1/2 cups potatoes and 1 cup broth to blender or food processor and process until smooth. (Process more potatoes for thicker consistency.) Return puree to pot and stir to combine, adjusting consistency with more broth if necessary.

Step 4

To make garlic chips, heat oil and garlic in 10-inch skillet over medium-high heat. Cook, turning frequently, until light golden brown, about 3 minutes. Using slotted spoon, transfer garlic to plate lined with paper towels; discard oil. Sprinkle lightly with salt.

Step 5

Season soup with salt and pepper to taste and serve, sprinkling each portion with chives and garlic chips