Put all the ingredients for the pickled beetroot in a medium, lidded saucepan. Pour over 800ml/1 pint 8fl oz water. The beetroots should be submerged, so add a little more water if you need to. Bring to the boil, then reduce the heat to medium and cook, covered, for 35–40 minutes, or until the beetroot is soft. Leave to cool completely.
Lift the beetroots out of the liquid, then peel and cut them into 1cm/½in dice. Put it in the bowl. Strain the pickling liquid, and return it to the pan. Cook over a medium heat for 25 minutes, or until reduced by half to about 600ml/1 pint 2fl oz. Set aside to cool, then pour the liquid over the beetroots. Cover and chill in the fridge for 24 hours.
For the bases, lightly grease eight 12cm/6in diameter ramekins or soufflé tins with melted butter and place a circle of baking paper in the base of each.
Put all the ingredients for the cheesecake base in a food processor. Pulse to form fine crumbs, then divide between the ramekins, pressing down evenly and firmly.
For the cheesecake toppings, preheat the oven to 200C/180C Fan/Gas 6. Melt the butter in a small saucepan over a medium heat for 7 minutes, stirring from time to time, until soft. Leave the leeks to cool, then transfer them to a large mixing bowl.
Add the cream cheese, crème fraîche, cream, garlic, chives, basil, salt and a good grind of black pepper to the leeks. Mix well to form a smooth paste. Gently fold in the blue cheese and eggs, then pour the mixture into the ramekins.
Bake for 25–30 minutes, until a skewer inserted into the middle comes out clean.
Serve immediately, in the ramekins or soufflé tins, garnished with a drizzle of honey, the hazelnuts and basil. The beetroot, strained, can be spooned on top of the cheesecakes before the garnishes, or served alongside.