Make the soup:
Heat the oven to 375°F. Put the garlic heads in a small baking pan. Drizzle on 2 Tbs. of the olive oil and sprinkle on the salt. Add 2 Tbs. water to the pan, cover with foil, and roast until a squeezed clove yields a soft purée, 30 to 45 minutes. When cool, squeeze the pulp from each clove.
In a soup pot over low heat, sweat the onion and leek in 1 Tbs. of olive oil until very soft but not brown, about 10 minutes. Add the potatoes and thyme and cook another 1 minute. Turn the heat to medium high, add the wine, and let it reduce to just a few teaspoons, about 4 minutes. Add the broth; bring to a boil. Reduce the heat and simmer for 10 minutes. Add the garlic pulp and simmer until the potatoes are very soft, another 15 to 20 minutes.
Strain the soup, saving both the liquid and solids. In a blender or food processor, purée the solids in batches, using some liquid to help it blend, and pour the puréed solids back in the pot. When all the solids are puréed, add as much of the remaining liquid as necessary to get a consistency like heavy cream. Season to taste with salt and pepper.
Sauté the cauliflower:
Heat 2 Tbs. oil in a large sauté pan over medium heat. Add the cauliflower florets and sauté. Once they begin to soften, after about 5 minutes, season with salt and pepper. Continue to sauté until the cauliflower is deep golden brown and tender but still firm, another 7 to 10 minutes.
Reheat the soup. Ladle it into individual bowls, add the cauliflower, and garnish with the sorrel or chives.