Arrange the sausages on a foil-lined grill rack and slide under a preheated, medium-hot grill for 15–18 minutes, or according to the packet instructions, until cooked through.
Cook the potatoes in a pan of salted boiling water for 12–15 minutes, until tender.
Meanwhile, melt half the butter in a frying pan and cook the sprouts with the nutmeg and a generous pinch of salt and pepper over a medium-low heat for 4–6 minutes, stirring occasionally, until softened.
Drain the potatoes, return to the pan and mash until smooth with the remaining butter. Stir in the chives, mustard, crème fraîche and sprouts and serve with the grilled sausages.