This recipe is based on our first use of Penelope Casas' recipe from ¡Delicioso! The Regional Cooking of Spain. It sounds like the flavor might be scary, but the garlic is cooked so long that it loses its vehemence. It's a very traditional soup here in Barcelona, especially around Christmastime.
She claims the secret is "the order in which the ingredients were combined" but I found it needlessly complex so I'm simplifying it here. I don't see any reason to create the water-garlic broth separately from adding the beef stock. Heating bowls of stock with the eggs in a hot oven to cook the eggs is a time/energy-waste and makes the bowls too hot to touch. I doubt it's critical to use 4.5 Cup of water but 4.0 Cup of stock, so I'm rounding to convenient metric units. Maybe it makes sense in the restaurant kitchen where she got the recipe, but it's unnecessary work for a home cook.
I also question whether we need water and stock: why not just use all stock for more flavor? Perhaps it would have too much mouth feel and get sticky with a good-quality homemade beef stock. I used a good Spanish boxed chicken stock because it's what I had, and I've seen many other recipes (including other Casas books) that use chicken stock.
Overview: make a garlic broth, toast the bread in garlic-infused oil to make croutons, serve in bowls filled with an egg, ham, broth, and croutons. There's a lot of broth so make sure your pot can hold 2 Liters.
Servings: 6; with the egg, ham, and croutons, it's a filling lunch.
Duration: 1 hour.
In a large pot, add the Oil and crushed Garlic. Sauté slowly until lightly browned and beginning to soften.
Add the Pimenton and Pepper to bloom briefly, then the Stock and Water.
Simmer slowly, covered, for 45 minutes to extract the Garlic flavor.
Taste and add Salt as needed.
Meanwhile, put the Oil and minced Garlic in a large wide skillet and slowly cook until the Garlic begin to take on just a little color; don't darken too much as you'll be heating it more with the bread.
Add the Bread pieces and sauté until they are crisp and golden, about 15 minutes; stop if the Garlic is getting too dark and acrid.
Remove from heat and add the Pimenton, stir to coat and bloom flavor.
To serve, crack an egg and slide whole into each bowl.
Top with Jamon.
Bring Broth to vigorous boil and pour over Egg and Jamon; the Egg should poach a little.
Top with Garlic Croutons.
Serve.