Preheat the oven to 200°c / 390°f.
Pour the olive oil into a large casserole dish or baking sheet and place in the oven to heat for 10 minutes.
Meanwhile put the potatoes in a large pan of boiling water and simmer for 8 minutes until they start to soften, but should not be cooked all the way through. Drain and set aside.
Remove the pan from the oven, then stir in the marmite.
Pour the potatoes into the dish and stir well until completely coated in the marmite and oil.
Scatter the rosemary sprigs and garlic cloves around the dish, then roast in the oven for 30 minutes. Turn the marmite roast potatoes halfway through.
Finally, add in the broccoli and stir. Season with salt and pepper and put back in the oven for a final 10-15 minutes.
