Fasolakia (Greek Stewed String Beans)

I found this recipe on a food blog called "Please, DON'T pass the salt!" and gave it a try. It was great! They say the recipe below is the old family recipe and then they make notations as to how to make it low-sodium.

A flavorsome combination of green beans stewed in a tasty tomato sauce. Simple, healthful, and delicious. A wonderful holiday alternative to the usual cream soup based green bean casseroles.

2 pounds string beans, fresh or frozen
2 onions, chopped
2 – 4 cloves garlic, minced
½ cup olive oil (I use about 1/4 cup now)
1 - 8 ounce can (no salt added) tomato sauce
¼ - ½ cup fresh parsley, chopped (I used 2 tbsp. dried parsley)
1-2 teaspoons mint (I used 1 tsp. each of dried mint, oregano, & dill)
2 potatoes, peeled and cut in 1-2 inch chunks (any kind of potato will work)
2 carrots, sliced
1 cup water or low sodium broth (I used low sodium chicken broth)
2 teaspoons salt (I omitted)
Pepper to taste

In Dutch oven, sauté onion lightly in olive oil. Add tomato sauce, string beans, and remaining ingredients. Cover and simmer over medium heat for about 60 minutes or until all vegetables are tender. Check after 30 minutes; add more water or broth if necessary. Serve hot or room temperature.