Preheat the oven to 180C/160C Fan/Gas 4.
Pierce the leg of lamb 10-12 times all over using the point of a sharp knife, then insert the lavender sprigs into the holes.
Use the hay to stuff a large, deep-sided roasting tray, one that’s large enough for the whole leg of lamb. Sprinkle over the remaining lavender leaves.
Place the leg of lamb onto the hay, then rub it all over with the softened butter, and season, to taste, with salt and freshly ground black pepper. Cover the roasting tray with aluminium foil.
Roast the lamb in the oven for 2-3 hours (for tender meat with a trace of pink), or until cooked to your liking, then remove it from the oven and set aside to rest for at least 30 minutes.
Meanwhile, bring the potatoes to the boil in a large pan of salted water and continue to boil for 2 minutes. Drain into a colander and shake them around to fluff up the edges.
When the lamb has about an hour left to cook, scrape the beef dripping into a large roasting tray, add the potatoes and season with salt flakes. Add them to the oven and roast for 25-30 minutes, or until golden-brown and crisp on their undersides, then turn them to coat them in the fat and continue to roast for a further 20-30 minutes, or until golden-brown and crisp all over.
Bring the vinegar and sugar to a simmer in a non-reactive saucepan, then remove the pan from the heat and stir in the chopped mint. Season with a pinch of salt.
Just before serving, cook the broccoli until just tender in a pan of salted, boiling water (about 2-3 minutes). Drain and season, to taste, with salt and freshly ground black pepper and a knob of butter.
To serve, transfer the lamb to a serving platter and carve into slices. Serve with the roast potatoes and purple sprouting broccoli alongside, and drizzle over the mint sauce.