Warm the olive oil in a wide heavy pot over medium heat. Sauté onion 5–7 minutes until softened.
Add garlic and potatoes; cook 3–4 minutes, stirring to coat.
Add green beans; stir 2–3 minutes to coat.
Stir in tomatoes, parsley, oregano, salt, and black pepper.
Pour in 250–300 ml hot water so it reaches halfway up the vegetables.
Bring to a gentle bubble, reduce heat to low, cover, and simmer 40–50 minutes until beans are very tender and potatoes are cooked through; uncover for the last 5–10 minutes if you want a thicker sauce.
Off the heat, stir in vinegar (if using). Taste and adjust salt. Serve warm or at room temperature.
Doneness test: beans should be very tender and potatoes easily pierced with a knife.