Season the lamb with salt and freshly ground black pepper, rub with half of the oil and press the rosemary on top. Heat a griddle pan until smoking, then grill the lamb steak for 3-4 minutes on both sides, or until golden-brown all over and cooked to your liking. Discard the rosemary and set aside on a warm plate to rest.
Heat the remaining oil in a pan and fry the fennel and aubergine over a medium high heat for 4-5 minutes, or until golden-brown. Season with salt and freshly ground black pepper.
Bring a pan of water to a gentle simmer and add a splash of vinegar. Crack the egg into a bowl. Swirl the water with a wooden spoon to create a whirlpool, then gently slide the egg into the middle. Poach for 3-4 minutes, or until the egg white is set and the yolk is still runny. Remove with a slotted spoon and drain on kitchen paper.
To serve, arrange the fennel and aubergine on a plate with the tomato slices in between the layers. Slice the lamb into three equal pieces and arrange on top of the vegetables. Finish with the poached egg on top.
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