Cook the pasta in a large saucepan of salted boiling water according to the packet instructions until al dente.
Meanwhile, spread the asparagus out on a baking sheet, brush generously with oil and season with salt and pepper. Place under a preheated hot grill and cook for 8 minutes, turning as they brown.
Cook the beans or peas in a separate saucepan of lightly salted boiling water for 2 minutes, then drain.
Drain the pasta. Pour the cream into the empty pasta pan over the heat, add the cooked beans or peas, the grilled asparagus and the Parmesan and season with salt and pepper. Return the cooked pasta to the pan, add the mint and toss well with 2 wooden spoons. Serve immediately with a scattering of Parmesan.