This recipe, inspired by Indian chutneys, creates a more complexly flavored sauce than old sweet-tart cranberry sauce made with back-of-the-bag instructions. Adding vinegar, aromatics, and spices to slow-cooked cranberries and fruit yield a jammy relish with kick and savor.
Heat oil in medium saucepan over medium heat until just shimmering. Add shallot, fresh ginger, and salt; cook, stirring occasionally, until shallot has softened, 1 to 2 minutes.
Add water, vinegar, and sugar. Increase heat to high and bring to simmer, stirring to dissolve sugar. Add 1½ cups cranberries and apples; return to simmer. Reduce heat to medium-low and simmer, stirring occasionally, until cranberries have almost completely broken down and mixture has thickened, about 15 minutes.
Add remaining 1½ cups cranberries and crystallized ginger; continue to simmer, stirring occasionally, until just beginning to burst, 5 to 7 minutes. Transfer to serving bowl and cool for at least 1 hour before serving. (Sauce can be refrigerated for up to 3 days.)