This chutney is sweet and spicy. Years ago a friend gave it to me after she served it at Thanksgiving and it has become a holiday staple. I have made it up to 4 days in advance and it keeps beautifully. After the holiday I have put it over vanilla ice cream; sounds strange but also delicious.
Combine sugar, orange juice, vinegar, ginger, orange zest, shallot, cinnamon sticks, and salt together in a skillet; bring mixture to a boil. Cook and stir until mixture thickens and sugar has dissolved, 8 to 10 minutes. Add cranberries; continue cooking and stirring until cranberries pop, about 10 more minutes. Remove from heat.
Heat vegetable oil in a small pan over medium heat; add mustard seeds. Cook and stir until mustard seeds begin to toast and pop, 1 to 2 minutes. Stir seeds into chutney. Serve chilled or at room temperature.