Cook the pasta according to the directions, before draining thoroughly. Meanwhile,
Trim or snap off the tough ends of the asparagus spears. Finely chop the asparagus together with one of the garlic cloves and also the herbs
In a small saucepan, bring the cream to a boil, along with the rest of the garlic cloves, simmering until the cloves are soft. Remove from the heat and discard the garlic
In a large saucepan, heat the olive oil and butter before adding about half of the chopped asparagus. Saute for ~ 5 minutes, stirring occasionally
To the pan, add the rest of the chopped asparagus, followed by the flavored cream
Bring to a boil before reducing the heat to a simmer until the cream begins to thicken, (~ 6-7 minutes)
Add the pasta to the sauce, along with about half of the Parmesan, and the lemon juice. Toss to combine
Season to taste with additional salt, lots of freshly ground black pepper. Serve with the remaining Parmesan