Remove all the cloves of garlic from the head.
Take a smallish saucepan and heat to boiling a cup of water; add the cloves of garlic and simmer for about 1 minute - drain, peel the garlic (which should be slightly softened and should peel easily) and cut each clove in half.
Add garlic cloves to beef broth in saucepan; cover and simmer 10 minutes, or until garlic is soft.
Remove half of the garlic cloves and reserve.
To the saucepan add the chicken broth, water, wine, half and half, thyme (crush it with your fingers before adding), and cayenne to broth and heat to a low simmer for 5 minutes.
With an immersion blender or in a regular blender, puree the soup; season to taste with salt and freshly ground pepper, set aside, and keep warm.
Toast bread on one side under broiler; remove and spread un-toasted sides with butter.
Mash the reserved half of garlic cloves and spread over the un-toasted and buttered sides of bread; sprinkle with shredded Gruyere cheese.
Broil toast until brown and bubbly, about 30 seconds (careful, they can burn easily).
Place a piece of toast in each of the four soup bowls; ladle hot soup over and serve.