Preheat the oven to 220°C.
Pulse all herb crust ingredients in a food processor to combine.
Heat oil in a frying pan until nearly smoking.
Season lamb racks with salt and pepper and fry until brown on all sides.
Brush the flesh side of each rack with mustard.
Press the herb crust mixture onto the mustard layer.
Roast lamb in a roasting tin for 20 to 25 minutes.
Heat olive oil in a frying pan over medium heat.
Fry shallots, celery, garlic, and carrot until softened.
Stir in the beans and crème fraîche off the heat.
Season bean mixture and transfer to a shallow ovenproof dish.
Mix breadcrumbs, parmesan, and melted butter, and sprinkle over beans.
Remove lamb from oven and rest under foil for 20 minutes.
Reduce oven temperature to 200°C.
Bake bean gratin for 20 minutes until golden.
Carve the lamb and serve with the bean gratin.