Pop the porcini in a heatproof dish. Pour 150ml boiling water over. Set aside to soak.
Lay the chicken breasts on a chopping board. Grate the zest from the lemon over them. Dust with a generous pinch of salt and pepper. Drizzle ½ tsp olive oil over each chicken breast. Rub the seasoning, zest and oil all over the chicken. Use a rolling pin or meat mallet to beat the chicken breasts flat. You want them to be 1-2cm thick. Set aside.
Peel and thinly slice the red onion. Peel and finely chop the garlic. Set a pan over medium heat. Add 1 tsp oil. Add the onions with a good pinch of salt and pepper. Lower the heat. Cook for 5 mins, stirring often.
Drain and rinse the beans. Add them to the onion, along with the garlic. Pour in the porcini and the soaking liquid. Gently simmer for 10 mins, adding a splash more water if you think the pan needs it. Cover and take off the heat to keep warm.
While the beans cook, trim the dry ends off the purple sprouting broccoli. Pick off the thick leaves and halve the stalks if they're very thick. Strip the sage leaves from the stalks. Press the sage into the chicken breasts on both sides.
Set a large frying pan over high heat. Add 1 tsp oil to the pan. Press the chicken into the pan. Cook on each side for 5 mins, or till golden and cooked through. The thinner you bashed it, the faster it'll cook. Once cooked, set aside on a clean chopping board to rest.
Add the purple sprouting broccoli to the pan along with 150ml water. Add a good pinch of salt and pepper. Cook till just tender, 3-5 mins. Add a good squeeze of lemon juice.
Taste the beans. Add more seasoning and a squeeze of lemon juice. Pile the beans on plates. Top with the purple sprouting broccoli and chicken to serve.