For the best texture, use freshly shredded cheddar rather than pre-shredded cheese, which often contains anti-caking agents that can make the soup grainy. If you prefer a chunkier soup, blend only part of the broccoli mixture and leave some florets whole. This soup keeps well in the refrigerator for up to 4 days and can be frozen in individual portions for up to 3 months; reheat gently over low heat, adding a splash of broth or cream if it thickens too much.