Brush the asparagus spears with a little of the oil. Cook in a preheated ridged griddle pan or under a preheated high grill, turning once, until charred and tender. Toss with a little more of the oil, half the lemon juice and salt and pepper. Set aside.
Cook the pasta in a large saucepan of salted boiling water for 8–10 minutes, or according to the packet instructions, until al dente.
Just before the pasta is cooked, heat the remaining oil in a large frying pan or wok over a medium heat. Add the garlic with a little salt and cook, stirring, for 3–4 minutes until softened but not browned. Add the chilli flakes and asparagus and heat through.
Drain the pasta, reserving a ladleful of the cooking water, and add both to the frying pan with the basil, remaining lemon juice, the Parmesan and pepper to taste. Serve immediately, with extra Parmesan, if liked.