For the purée, place the garlic and white wine vinegar into a small saucepan and cook until the garlic is tender. Drain and set aside.
Place the potatoes into a large saucepan of water and bring to the boil. Cook for around 15 minutes, until done, and drain.
Put the potatoes and garlic through a ricer into another saucepan and add the olive oil and double cream and mix until you have a smooth wet consistency.
Mix the soy, mirin, brown sugar and lemon juice together and add the mackerel to the mixture. Heat a medium frying pan and add the oil, place the fish in the pan and cook each side for 1-2 minutes. Spoon over the remaining marinade while cooking.
Heat a large saucepan of boiling salted water and blanch the purple sprouting broccoli.
For the dressing, place all the ingredients into a bowl and mix or place into a food processor and blend. Just before serving add the dressing to the broccoli and mix.
Place a spoonful of the purée onto a serving plate or bowl. Place the mackerel on top and garnish with the broccoli.