40 cloves garlic (2 heads)
4 c chicken stock
3 green onions, chopped
1 large onion, cut in half rings
1/4 c cream (you may want a little more)
1/4 c parmesan cheese
2 T fresh basil, chopped (or thyme)
2 T cornstarch or 2 eggs
Optional, but it adds a slightly different flavor than unbaked garlic: Place 2/3s of the garlic cloves (unpeeled) in a small oven-proof dish that has a tight-fitting lid. Toss with 1 to 2 T of olive oil. Cover and bake 45 minutes at 350. Cool. Squeeze each clove to extract the garlic. Set aside.
Peel [rest of] garlic. Slice. You want to maximize the cut edges to release the taste, so slice each clove into four pieces; cut the other way to turn them into matchsticks, if you like.
Sauté onions in a little oil until translucent; no need to brown. Add sliced garlic. Cook 3 minutes until garlic is soft-ish but not done. Watch! You do not want browned garlic! (If it is brown, start over. There's no way to save scorched garlic.)
In a soup pot, combine sautéed onions and garlic, [roasted garlic,] and stock. Simmer until sliced garlic is tender.
Purée. A blender works much better for this than a food processor. You'll have to work in batches. You may be able to use an immersion blender; it depends on how much power yours has.
Return purée to stock pot. Add cream and cheese. Bring to serving temperature. Adjust salt (you might not need any if you used commercial stock - it's quite salty) and add pepper to taste.
To thicken: Mix cornstarch with the smallest amount of water possible to from a slurry. Pour into hot soup, whisking constantly.
This soup works equally well as a sauce; reduce liquid (start with 1 can stock + 1 soup-can of water). It's wonderful on pasta, chicken, etc. Try a "white lasagna" and use this soup as the sauce.