Heat your oven to 180°C/Fan 160°C/ Gas 4. Scrub the sweet potatoes and slice them into chips approximately 1cm across. Place on a baking tray. Drizzle over ½ tbsp olive oil and toss to mix. Season with salt and pepper and roast for 25-30 mins.
Put a pan of water on to boil. Pop the broad beans from their pods. Add them to the pan. Simmer for 2 mins, then drain them. Rinse under cold water. Squeeze the loose grey skins to pop the green beans out (this is optional, as the grey skins are edible, but it will give you a sweeter, greener side dish).
Roughly chop the broccoli into small florets. Thinly slice the stalk. Trim the roots off the spring onions. Thinly slice it.
Place the broccoli in a pan. Sprinkle over ½ tsp salt. Pour over enough boiling water to just cover the broccoli. Cover with the lid and boil for 3 mins till the broccoli just starts to soften. Add the broad beans and spring onions to the pan and cook for another 2 mins. Drain. Set aside.
Place the fish on another baking tray or oven dish. Roughly chop half the dill and scatter over the fish. Finely grate half the lemon zest over the fish. Season with salt and pepper. Drizzle over 1 tsp olive oil and squeeze over the juice from half the lemon. Bake for 5-8 mins on the shelf above the chips, till flaking.
While the fish cooks, place the bean mixture in a food processor, or use a hand blender or masher, to coarsely blend the veg. Add the mint leaves and remaining dill and blend again (chop the herbs if using a masher and mix them in).
Serve each fish fillet with a large dollop of mushy beans, the chips and a lemon wedge to squeeze over.