Begin by preparing your vegetables. Finely chop the onion, mince the garlic cloves, dice the tomatoes, peel the potatoes, and trim the green beans, cutting them into 2-inch pieces. Having all your ingredients ready before you start cooking will make the process smoother.

Heat a large, deep skillet or Dutch oven over medium heat. Add 1 teaspoon of olive oil and swirl to coat the bottom of the pan.

Once the oil is hot (it will shimmer slightly), add the chopped onion. Cook for about 5 minutes, stirring occasionally, until the onion becomes translucent and soft. Add the minced garlic to the softened onions and cook for another minute, stirring constantly. Garlic cooks quickly and can burn easily, so keep a close eye on it.

Next, add the diced tomatoes and tomato paste to the pan. Stir well to combine all the ingredients. Cook this mixture for about 5 minutes, stirring occasionally, until the tomatoes start to break down and release their juices. Squeeze the juice of one lime into the tomato mixture.

Add the potatoes to the pan, stirring to coat them with the tomato mixture. Cook for about 5 minutes, allowing the potatoes to start softening.

Now, add the prepared green beans to the pan. Stir to combine all ingredients ensure the beans are well-coated with the tomato mixture.

Pour in 1 cup of water. Bring the mixture to a gentle boil. Once boiling, reduce the heat to low, cover the pan with a lid, and let the stew simmer. Cook for about 30-35 minutes, stirring occasionally to prevent sticking. The dish is ready when the green beans and potatoes are tender when pierced with a fork.

Taste the stew and add salt and pepper as needed. Remember, you can always add more seasoning, but you can't take it away, so start with a little and adjust to your taste.

Once seasoned to your liking, remove the pan from the heat. Let the fasolakia rest for about 5 minutes before serving.