Thinly slice the leeks and wash to remove any dirt or debris (see how to clean leeks).
Melt the butter in a frying pan over a medium heat. Add the sliced leeks and cook, stirring often for a few minutes.
Reduce the heat, cover the pan with a lid and let the leeks soften and ‘sweat’ for 7-10 minutes, stirring often. Check often so they don’t brown or scorch in the pan.
Increase the heat to medium and stir in the cream, blue cheese, mustard, salt and pepper. Stir until the cheese melts and the sauce thickens.
Serve warm as a side dish, or on slices of toasted sourdough.