Prepare the onion, garlic, tomatoes, and potatoes: Finely chop the onion and garlic. Peel the potatoes and cut them into small pieces. If using fresh tomatoes, chop them as well.
Sauté the onion: Heat 8 tablespoons of the olive oil in a large skillet or pot over medium heat. Add the onion and sauté for 1–2 minutes.
Add the garlic and continue to sauté until the onion is translucent. The onion and garlic should not brown.
Add the tomatoes: Add the tomato paste and tomatoes and stir well.
Add the potatoes, water, and seasonings: Add the potatoes, water, salt, some black pepper, oregano, thyme, and bay leaf. Cover and simmer for about 15 minutes.
Prepare the green beans: While the potatoes are simmering in the tomato sauce, trim both ends of fresh green beans and cut very long beans in half. Frozen green beans can be used straight from the freezer.
Add the green beans: Add the green beans, cover, and simmer everything together for another 20 minutes, until the potatoes and green beans are beautifully soft. Stir occasionally and check whether you need to add a little more water. The vegetables shouldn’t be swimming in water, but the pan shouldn’t be completely dry either – a little sauce is exactly what we want.
Finish with olive oil: Once the green beans and potatoes are beautifully soft, turn off the heat and stir in the remaining 2 tablespoons of olive oil.
Serve the Fasolakia with fresh white bread for mopping up the wonderful Lathera sauce and vegan feta, if you like.