To make the chraimeh sauce, mix the garlic, paprika, caraway, cumin, cinnamon, and oil in a small bowl. Return the large sauté pan to medium-high heat and, once hot, add the garlic and spice mix. Fry for about 1 minute, then add the tomato paste, sugar, lime juice, and ¾ tsp of salt. Stir to combine, then pour in 1 cup of water to make a thin sauce. Once bubbling, stir frequently for about 2 minutes, until the sauce begins to thicken. Return the green beans to the pan and continue to cook for another 1 minute, until the sauce is thick and the beans are hot.