Make 3 deep slashes in the top of each chicken breast and place them in a non-metallic dish. Mix together the pesto and mascarpone, pour over the chicken and leave to marinate for 10 minutes.
Heat a griddle pan or frying pan until hot and cook the chicken breasts for 3–4 minutes on each side until cooked through. Pour over any remaining marinade and heat through for 1 minute.
Meanwhile, cook the potatoes in boiling salted water until tender. Drain and toss through the crème fraîche, mustard and spring onions, and gently crush with the back of a fork.
Cook the beans in a small saucepan of boiling water for 2 minutes and drain. Heat the oil and butter in a frying pan, add the garlic and fry for 1 minute, add the beans and stir-fry for 1 minute. Serve the chicken with the potatoes and beans.