Chop the onion, carrot, and bell pepper into bite-sized pieces.
Trim the green beans and cut them in half.
Heat the oil in a large pan and sauté the onion, carrot, and bell pepper until softened.
Add the minced garlic and cook for another minute.
Stir in the green beans and chopped tomatoes.
Fill the empty tomato can with water and add it to the pan.
Season with salt and pepper.
Simmer for 20–30 minutes, until the green beans are tender but still hold their shape.
Stir in the chopped dill just before serving.
Serve hot with crusty bread.