Ham Broth:
1 tablespoon neutral cooking oil
1 large yellow onion peeled and quartered
3 heads garlic halved cross-wise, skin left on
3 pounds smoked ham hocks
9 cups water
Soup:
1 teaspoon neutral cooking oil
¾ pound loose chorizo or hot Italian sausage
1 yellow onion peeled and diced
¼ cup white wine optional, or use water
2 cups water plus more, if needed
1½ pounds Yukon gold potatoes scrubbed and quartered
6 sprigs thyme
2 pounds fresh string beans trimmed
Salt and pepper to taste
½ teaspoon paprika
½ teaspoon cayenne powder optional
Freshly minced parsley optional, for garnish