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Step 1
Heat olive oil in a Dutch oven over medium heat. Sauté onion and garlic until just softened, about five minutes.
Step 2
Add in the green beans, broth, and ham hock. Add water until it just covers the beans. Bring to a boil and then reduce heat and simmer for 35-45 minutes, or until the cooking liquid turns a deep green/brown and beans are well-done.
Step 3
20 minutes into simmering, add potatoes and additional ham, if using.
Step 4
Remove ham hock or ham bone, chop ham off the bone, and return to the pot—discarding the bone. Season with salt and pepper to taste.
Step 5
Serve by straining cooking liquid using a slotted spoon.