Heat olive oil in a skillet over medium heat. Add onion and cook for 20 seconds until nearly translucent. Add garlic, salt and pepper. Saute for another few seconds. Add sliced carrot and saute another 4 minutes.
Add the green beans and stir fry for 1 minute or until they brighten in color. Add the tomatoes and stir well. Add the water and sugar.
Bring to a boil, cover and reduce to a simmer. Braise for 30 minutes or until the beans are very soft and the tomatoes have formed a thin sauce. Season with more salt and pepper if necessary and remove from heat. Transfer beans onto a platter and allow them to cool before serving with yogurt and lemon wedges, if desired.
Notes
These beans can be made the day before and served cold as a salad.