Place the unpeeled garlic cloves in a mortar and crush them with a pestle, or put them in a small plastic bag and pound them with a rolling pin . Put the garlic, skins and all, in a heavy 4-quart soup pot and add the onion, water, salt, thyme, and bay leaf. Bring to a boil, reduce the heat to low, partially cover, and simmer slowly for 30 minutes.
Preheat the oven to 250 degrees F.
While the garlic simmers, place the croutes on baking sheet and sprinkle with the grated Cantal cheese. Reserve. Place 6 soup plates in the oven to heat.
Put the butter in a bowl and mash with a wooden spoon until it is a soft paste. Add the flour and egg yolks and combine thoroughly.
At the end of the garlic cooking time, strain the garlic broth through a fine-mesh sieve and return it to the pot. Slowly, a few tablespoons at a time, add 1 to 1 1/2 cups of the hot broth to the butter-egg mixture, whisking to combine thoroughly. Off the heat, put the egg-broth mixture into the pot, stirring until the soup is creamy and thoroughly blended.
Remove the soup plates from the oven and increase the oven temperature to 400 degrees F. When the oven is fully preheated, place the baking sheet with the cheese-covered croutes, in the oven for a few moments to melt the cheese.
Add the white wine to taste to the soup and place over low heat, stirring occasionally. Do not allow the soup to boil. Taste and add more salt if needed.
When thoroughly heated, remove the soup from the heat. Place the cheese-glazed croutes in the bottom of the heated soup plates and top with the hot soup. Serve immediately.
For croutes, the oven method is foolproof. Slice French bread into thin ovals (best for cream soups), and slice country, whole-grain, or rye bread into thicker slices or half slices (best for chunky, country-style soups). Spread each side of the bread with a very thin layer of fat. Place the slices in neat rows on a baking sheet and place in a 350 to 400 degrees F oven. In 5 minutes, check the bottom of a bread slice (the bottom will brown more quickly than the top because of its contact with the hot metal baking sheet). As soon as the bottoms are golden brown (5 to 8 minutes), take the baking sheet out of the oven. Turn all of the bread slices over and return them to the oven. This time the browning takes less time, 3 to 5 minutes. Remove from the oven and cool the croutes on a rack.
Store the croutes in a sealed canister. They will keep for several weeks.