Cook the pasta in a large saucepan of salted boiling water according to the packet instructions until al dente.
Meanwhile, heat the oil in a saucepan over a medium heat, add the garlic and shallots and cook, stirring, for 3 minutes. Add the peas, beans, asparagus and spinach and cook, stirring, for 2 minutes. Stir the cream into the vegetables and simmer for 3 minutes.
Drain the pasta thoroughly, then add to the vegetable mixture and season well with salt and pepper. Add the Parmesan and mint and toss thoroughly with 2 spoons. Serve immediately