Cook the new potatoes in a large pan of boiling salted water for 8-10 mins until tender. Add the green beans and spring greens for the last 3 mins. Drain, then separate the greens from the potatoes.
While the potatoes are cooking, cut the chicken breasts through the centre lengthways, leaving one side attached so it opens out like a book. Brush each one with 1 tsp of the olive oil, then season.
Heat a large frying pan over a medium-high heat and cook the chicken for 4 mins on each side until golden. Pour over the stock, capers, lemon juice and zest, then simmer gently for a few minutes to reduce. Add the cooked potatoes and simmer for another minute.
Heat the remaining 1 tsp oil in another frying pan and fry the garlic for 1 min until lightly golden and fragrant. Tip in the drained greens, and toss in the garlicky oil. Season, then scatter over the parmesan and serve with the chicken and potatoes.