1- Cut the asparagus so that it is all the same length, peel with a potato peeler, preferably a swivel peeler, to remove the toughest, woody parts, wash carefully under running water and dry on kitchen paper; separate the tips from the stalks, blanch the tips for 2 minutes in a little boiling salted water, drain and keep on one side as a garnish; cut the stalks into thin rounds.
2- Peel the shallot, wash, dry and chop finely, fry on a low heat in a frying pan with 30 g butter for about a minute, without browning; add the rounds of asparagus and allow them to absorb the flavours on a medium heat for 2-3 minutes, stirring gently with a wooden spoon.
3- Add a pinch of salt and plenty of ground pepper, pour in about one glass of hot water and continue to cook, covered on a medium heat for 15 minutes, stirring often and adding extra warm water if the contents on the bottom of the pan become too dry.
4- Put half of the rounds of asparagus through the vegetable mill, transfer the purée back to the frying pan and add the cream; put the mixture back on the heat until it becomes a smooth, thick sauce, stirring all the time.
5- Remove the skin from the sausage and cut into equal-sized pieces; fry on a high in a non-stick frying pan for 4-5 minutes without any oil, stirring often to prevent the sausage from sticking to the bottom of the pan.
6- Cook the tagliolini until the pasta is "al dente" in plenty of salted water with oil, drain, leaving the tagliatelle a little wet and add the sauce, the rest of the rounds of asparagus and the sausage pieces; garnish with the asparagus tips kept on one side, sprinkle evenly with Parmesan cheese and serve.