Put the apples, onions, vinegar, sugar, jalapeño, orange zest and juice, coriander, cumin, ginger, salt, allspice, cinnamon, and cayenne (if desired), in a medium pot over medium-high heat.
Cover and bring to a boil, then adjust the heat so the mixture simmers gently.
Cook, stirring occasionally, until the mixture is very thick and the apples have broken down completely, about 1 hour.
Serve warm or at room temperature.
(Store leftover chutney in an airtight container in the refrigerator for up to a week.)
