Method:
Trim the tough ends from the asparagus and chop finely. Chop one garlic clove and herbs, separately, and reserve.
In a small pot bring the cream to a boil with the rest of the whole garlic cloves and simmer until they are soft. Remove from the heat and discard the garlic.
In a wide saucepan heat the olive oil and butter and fry half of the chopped asparagus for around 5 minutes, stirring every now and then. Add the rest of them, along with half the herbs and the chopped garlic. Follow with the flavoured cream. Bring to the boil and then simmer until the cream starts to thicken, around 5 minutes. Remove from the heat, season with salt and pepper (you'll be adding more salt with the parmesan so keep this in mind). Keep warm.
Cook the pasta in salted water as per package instructions (usually 11 minutes for al dente tagliatelle), drain, keeping a cup of the cooking water, and add the sauce along with half the Parmesan and the lemon juice. You might need to add a bit of pasta water to get to a saucy consistency, remember pasta keeps absorbing liquid as it cools down. Serve with remaining Parmesan and chilli oil drizzle over the top.