Cut the top off a whole head of garlic. Drizzle the head with olive oil, salt, pepper and wrap it entirely in foil. Bake in a shallow dish in a preheated 400 degree oven for 40 minutes. Allow to cool slightly, then the roasted garlic cloves will pop right out of the head.
Heat the butter and oilive oil over medium heat in a Dutch Oven. Add the sliced shallot and soften for 3 minutes. Smash all of the garlic cloves (roasted and raw). Add to the Dutch Oven and cook for an additional 2 minutes.
Pour in the warm chicken stock and spices and cook for 5 minutes. Lower the heat to simmer and cook for 10 minutes. Remove the bay leaf. Use an blender to smooth the soup (or an emersion). You may have to work in batches and allow for some cooling first to use a blender.
Pour the puree of soup back into your Dutch Oven (still on simmer). Add the heavy cream and stir briefly to incorporate into the soup. In a small bowl or cup, whisk the egg yolks with the red wine vinegar. Lightly whisk the egg whites in a separate small bowl or cup.
Drizzle and whisk the egg whites into the soup, stirring and allowing for stringy consistency. Then temper the yolks with a small amount of soup and drizzle into the soup in the same manner, stirring constantly. Add salt and black pepper, raise the heat to medium, and cook for 5 minutes.
Serve in a cup with a garnish of thyme leaves and shredded Gruyere cheese.
A unique garnish, and very French, would be to add a tablespoon of red wine to each cup of soup before serving. Let your guest stir and add their own cheese.
To cut your time, you can skip roasting the one head of garlic and simply use two heads smashed. The roasted garlic is in the recipe to add some sweetness and cut some of the natural bitterness of the garlic.
Serve with extra shredded cheese in a side dish for guests to add to their taste.