From Ruth Rogers of River Café London: Thirty Years of Recipes and the Story of a Much-Loved Restaurant cookbook: "We cook this pasta when asparagus is in season and we cut them almost as thin as the tagliarini."
Trim or snap off the tough ends from the asparagus spears. Finely chop the asparagus all together with one of the garlic cloves and the herbs.
Bring the cream to the boil in a saucepan with the rest of the whole garlic cloves and simmer until the cloves are soft. Remove from the heat; discard the garlic.
Heat the olive oil and butter in a separate large saucepan and saute half of the chopped asparagus for 5 minutes, stirring. Add the rest of the chopped asparagus followed by the flavored cream. Bring to the boil, then reduce the heat and simmer until the cream begins to thicken, about 6 minutes. Season. Remove from the heat and keep warm.
Cook the pasta in a generous amount of boiling salted water, then drain thoroughly. Add to the sauce along with about half of the Parmesan and toss together. Serve with the remaining Parmesan.