Cut the tips off the asparagus and reserve. Cut the stalks into 2.5 cm (1 inch) pieces and blanch in a saucepan of boiling water for 3–4 minutes until very tender. Drain and put in a food processor with the garlic, oil and Parmesan. Process to make a smooth paste. Season with salt and pepper.
Arrange the bacon rashers in a single layer on a baking sheet and cook under a preheated hot grill for 5–6 minutes until crisp and golden. Break into 2.5 cm (1 inch) lengths.
Meanwhile, cook the pasta in a large saucepan of salted boiling water according to the packet instructions until al dente, adding the reserved asparagus tips to the pan 3 minutes before the end of the cooking time.
Drain the pasta and stir into a bowl with the asparagus sauce. Scatter with the crispy bacon and Parmesan shavings and serve immediately.