Heat the oil in a pan; cook the chicken for 5 minutes. Add the onion and garlic; cook for a further 5 minutes. Stir in the crème fraîche, mustard, ¾ of the cheese, the chives and the mint, then cook for 2 minutes until the chicken is cooked through with no pink remaining.
Meanwhile, bring a pan of water to the boil and add the broad beans. Cook for 2 minutes, drain, and skin.
Bring another large pan of water to the boil, add the pasta and cook for 8-10 minutes, adding the peas and asparagus for the last 2 minutes. Drain, reserving 200ml of the water. Tip the pasta, peas, beans, asparagus and the water into the chicken mixture and stir to combine.
Season with freshly ground black pepper and serve with a squeeze of lemon and the remaining cheese.