Peel and finely slice the garlic, then pick the basil leaves and finely chop the stalks.
Cook the tagliatelle in a pan of boiling salted water for 8 to 10 minutes, or until al dente, which means that it should be soft enough to eat, but still have a bit of bite and firmness to it, then drain, reserving some of the pasta water.
Heat a lug of olive oil in a saucepan over a medium heat, add the garlic and fry for 1 to 2 minutes, or until golden.
Add the basil stalks and tinned tomatoes, breaking the tomatoes up with the back of a spoon.
Bring to the boil, season with sea salt and black pepper and simmer for 5 minutes.
Snap the woody ends off the asparagus and discard, then finely chop the spears.
Add the asparagus to the tomato sauce, simmer for 1 to 2 minutes, then remove from the heat and season to taste, if needed.
Finish off the sauce by stirring through the basil leaves. Toss the tagliatelle in the sauce, adding a little cooking water to loosen, if needed.
Serve with a drizzle of extra virgin olive oil and a good grating of Parmesan. Enjoy!