This is the dish known as "Lubyi bi Zayt" in Arabic, or Green Beans in Olive Oil. Recipes vary widely - by cook, by village, by region of Lebanon. Sometimes a housewife might add a little chopped meat to the browning onions. Sometimes the dish might have a hot chili, or lemon juice, or allspice, or tomato paste. The basic idea is to saute and then braise green beans with tomatoes, onions, and garlic. The following recipe is a loose version of what I do.
1 1/2 pounds green beans, ends snapped, strings removed, beans snapped in half
1 large onion, chopped
1/2 cup olive oil (you can use less but it affects flavor and texture)
3 or 4 cloves of garlic, crushed or minced fine (some recipes use lots more garlic, peeled only, not cut)
1 1/2 pound tomatoes (4 large?), peeled and cut into chunks, or 1 28 oz can, drained
pinch of sugar
Saute the onion in olive oil on medium heat until translucent. Add green beans, saute until they get a bit of color and onion turns golden. Add garlic, saute another minute, then add tomatoes, salt (1/2 tsp? - to taste), black pepper, 1/4 tsp. allspice and a pinch of sugar. Okay the measurements here are to taste, very elastic. Bring the tomatoes to a boil, turn down heat, cover the pan and simmer until tender. Time is controversial - Middle Easterners like their green beans very soft. I go for 20 minutes, checking at 15; some Arabic recipes say 35 minutes. You be the judge.
The classic dish wants the green beans to absorb the tomato completely, whereas my version allows the tomatoes and green beans to still retain their shapes and identity. I don't claim my recipe is definitive. It may suit a Blue State palate more than the classic version. Here are some others I found:
Lebanese Green Beans at the Tripoli food site.
A recipe from the 1950s, via Al-Mashriq