Preheat the oven to 200C / 400F.
Brush the sweet potato halves on the open side with oil, then place them face down on a baking tray lined with parchment paper or foil. Brush the skins with a little oil and poke a couple of holes in each one with a knife. Place in the oven on the top shelf for 20 minutes.
Meanwhile, prepare the broccoli by tossing it with the spices, salt and pepper to taste and enough olive oil to lightly coat the florets (3-4 tablespoons should be about right).
After 20 minutes, move the sweet potatoes in the oven to the lower shelf. Scatter the broccoli onto another baking dish and place in the oven on the top shelf. Bake for a further 15-20 minutes until the broccoli is browned and crisp and the sweet potatoes are soft through.
Remove the broccoli and sweet potatoes from the oven. Mix the lemon zest through the broccoli dish and then squeeze the 1/2 lemon's juice on top and mix again.
Flip the sweet potatoes over and lightly mash with some butter.
Scoop the broccoli over the top of each sweet potato half, adding dollops of goat cheese throughout.
Cover with the grated cheese and place back in the oven for another 5-10 minutes, until the cheese is melted to your liking.
Serve with a scatter of fresh herbs if using.