Preheat the oven to 180 C fan/200 C/gas 6. Lightly grind the coriander seeds and black peppercorns in a pestle and mortar, then add them to a medium roasting tin along with the carrots, olive oil, water and 1/2 teaspoon salt. Cover with foil, then roast in the oven for 40 minutes.
After 40 minutes, remove the foil, drizzle the carrots with the agave or maple syrup, then return to the oven for a further 15 minutes to reduce the liquid and get some colour on the carrots. Put the hazelnuts on a small baking tray and pop them into the oven at the same time to toast.
Meanwhile, put the olive oil, lemon zest, coriander seeds, spring onions and garlic into a small frying pan and warm through over a low heat for 5 minutes - you're not aiming to get any colour on the garlic, so keep the heat down.
Put the butterbeans and the infused oil, spring onions etc, into a high-speed blender or food processor and blitz until very smooth. Add a squeeze of lemon juice, then taste and adjust the salt if needed. warm the mash and spoon into shallow bowls, topped with the roasted carrots. Scatter the carrots with a little sea salt, the toasted hazelnuts and flat-leaf parsley and serve warm.