For the mussels, kumquats and rosemary. Heat the vegetable oil in a deep-fat fryer or a deep-sided, heavy-bottomed pan to 180C, or until a breadcrumb sizzles and turns golden-brown when dropped into it. (CAUTION: hot oil can be dangerous. Do not over-fill the pan or leave unattended).
Pick the top heads off the rosemary sprigs and put in the hot oil, remove straight away with a slotted spoon and drain on kitchen paper. Set aside.
Mix the semolina and polenta. Pat the mussel meat dry and toss in the semolina and polenta mix to coat, shake off any excess.
Increase the deep-fat fryer temperature to 190C. Put the mussels in the deep-fat fryer, fry for 1-2 minutes, or until crispy. Remove and drain on kitchen paper. Season with fine salt and toss with the kumquats and rosemary.
For the anchovy dressing, put all the ingredients in a food processor and blend.
For the purple sprouting broccoli, remove the woody ends and leaves, reserve the leaves. Slice the stems vertically, taking care to keep the florets attached. Put under a damp cloth and set aside.
Put the capers, reserving a few for garnish, the Parmesan, rosemary and a pinch of salt in a bowl and mix.
Put the butter in a saucepan, melt until it bubbles and turns nutty brown. Keeping on a low heat, add the focaccia and toss every so often until the bread is evenly dark-brown. Remove the bread with a slotted spoon and put on a tray. Sprinkle the capers and Parmesan mix over the bread while it is still hot so that it sticks to the bread.
Put the broccoli in a large bowl, spoon over a little dressing to coat the florets and leaves. Fold through the capers, torn anchovies, croûtons and a couple of shaves of Parmesan. I crush a little extra bread to garnish and a few more Parmesan shavings and finish with extra virgin olive oil.
Serve the fried mussels on a serving platter and season. On a separate plate, serve the coated broccoli garnished with the reserved capers.