Chop the asparagus into 3 cm pieces - put the tips aside. Finely chop the onion.
Heat the oil over medium heat in a saucepan. Add the onion and sauté for about five minutes or until softened. Add the garlic and the chopped asparagus and sauté for another minute.
Add vegetable stock. Bring to a boil, lower heat and simmer 5 ten minutes. Add half the beans, then turn off the heat. Add most of the dill. Using a stick blender, process the soup until smooth and creamy. Add the remaining beans and the asparagus tips. Bring the boil and cook for 2-3 minutes. Add more stock if it's too thick.
Season with salt and pepper. Serve with a squeeze of lemon juice, garnished with some dill leaves.