Heat a dry frying pan. Fry the almonds on medium heat in about 3 minutes until golden brown. Cool on a plate.
Chop the onion and finely chop the garlic. Finely chop the basil.
Heat 2 tablespoons of olive oil in a frying pan. Fry the onion and garlic. Pour in the wine to deglaze the pan and leave on a high heat for 2 minutes to reduce. Add the cooking cream and simmer the sauce on a low heat.
Add the basil. Leave to simmer for another 3 minutes. Season with salt and pepper.
Meanwhile, cook the tagliatelle according to the instructions on the package.
Brush the asparagus with the rest of the olive oil. Heat the grill pan (or frying pan) and grill the asparagus in about 2 minutes al dente.
Divide the tagliatelle over the plates. Pour over the sauce, then add the asparagus. Sprinkle with Parmesan cheese and the flaked almonds.