Peel and finely chop the onion. Trim and finely chop the carrot and celery to match the onion. Place a large pan on the heat for 2 mins then drizzle in ½ tbsp olive oil. Add the chopped veg with a pinch of salt and fry on a low heat for 10 mins, stirring often, till softened and browned.
Meanwhile, peel and cut the potato into 1cm-thick cubes. Peel and grate or crush the garlic. Drain and rinse the beans. Fill and boil the kettle.
After the veg has cooked for 10 mins, add the potato and garlic to the pan and fry, stirring, for 2 mins. Tip in the beans. Pour in 600ml hot water from the kettle. Bring to a bubble, cover and simmer for 10 mins.
While the soup simmers, zest the lemon into a blender or processor. Roughly chop the wild garlic and dill stalks (keep the fronds separate) and add them too. Pulse a few times then pour in the cream. Pulse till the mixture is a vibrant green. Alternatively, chop the wild garlic and dill as finely as possible then stir into the cream with the lemon zest.
When the soup has simmered for 10 mins, pour in half the wild garlic cream and stir. Simmer for 2 mins. Blend the soup briefly for a slightly chunky soup, or blitz till smooth. Taste the soup and add more salt, or some pepper if you think it needs it, or squeeze in a little lemon juice.
Ladle the soup into warmed bowls. Swirl the rest of the wild garlic cream through the soup and tear over the dill fronds to serve.