When I worked at River Cottage, we’d instinctively make remouillage, or a second stock, from bones that had already been boiled for stock. The rich stock ingredients had heaps of flavour left in them even after being cooked and strained, so we’d refill the pot with water and make a second, weaker stock to use in soups, for boiling greens or to make boulangère potatoes. We’d also make fresh bone stock in remouillage rather than water, creating a very potent jus.
