How to Make It
In a large saucepan, melt 2 tablespoons of the butter in the olive oil. Add the shallots and cook over low heat until softened, about 5 minutes. Add the chopped asparagus, season with salt and pepper and cook, stirring, until softened, about 5 minutes. Add the chicken stock and cream and bring to a boil over moderately high heat. Reduce the heat to moderately low and simmer until the asparagus is very tender, about 15 minutes.
Meanwhile, bring a medium saucepan of water to a boil. Add salt and the asparagus tips and cook until just tender, about 3 minutes. Using a slotted spoon, remove the tips and reserve them; keep the water boiling.
Puree the soup in batches in a food processor and strain it through a coarse sieve, pressing on the solids. Return the soup to the large saucepan, season with salt and pepper and add the asparagus tips. Keep hot.
Add the Lemon Dumplings to the boiling water and cook until just tender, about 1 1/2 minutes; drain. Melt the remaining 2 tablespoons of butter in the saucepan over moderately high heat. Add the dumplings and carefully swirl them in the butter to coat. Add 4 dumplings to each soup plate, ladle the asparagus soup over them and serve.