Preheat the oven to gas 200C/400F/Gas 6.
Place the carrot juice and ginger juice into a pan over a medium heat and bring to the boil. Cook to reduce to about 150ml/5fl oz of liquid, then slowly whisk in 30g/1oz of the butter. Season, to taste, with salt and freshly ground black pepper and set aside.
Heat a frying pan and add 50g/2oz of the butter and the olive oil. Add the potatoes and fry over a high heat until starting to become golden-brown.
Add the herbs and garlic and continue to fry until the potatoes are cooked through.
Heat a clean frying pan until hot, add the rapeseed oil and remaining 30g/1oz butter. Once the butter is foaming, add the pork fillets and fry, turning occasionally, until golden-brown on each side. Season, to taste, with salt and freshly ground black pepper.
Remove from the pan and place onto a plate. Drizzle with the honey and coat well with the sesame seeds.
Transfer the honey and sesame-coated pork fillets to a trivet in a roasting tray and place into the oven to cook for 10-12 minutes, or until completely cooked through. Remove from the oven and leave to rest in a warm place for five minutes.
To serve, carve the pork into thick diagonal slices. Spoon the potatoes into the centre of each plate. Top with the pork and spoon over the carrot and ginger sauce.
