Wash the orange under running water before peeling or juicing. Use a vegetable peeler to take 4 broad strips of peel with minimal white pith. Measure the orange juice separately, removing seeds. Peel and thinly slice the ginger.

Combine apple cider, orange juice, orange peel, cinnamon sticks, whole cloves, and ginger in a 3- to 4-quart saucepan. Heat over medium-low heat for about 8–10 minutes, until steaming with small bubbles at the edges. Do not bring to a rolling boil.

Reduce the heat to low, partially cover, and gently infuse for 20 minutes. Keep the liquid hot without boiling hard. Remove from the heat and taste a cooled spoonful; strain promptly when the spice level suits you.

Carefully pour through a fine-mesh strainer into a heatproof pitcher or another pot. Remove and discard the peel, cloves, cinnamon, and ginger; do not serve the hard whole spices in mugs. Divide the finished batch into 8 equal servings, approximately 1 cup each. Let servings cool to a comfortable drinking temperature.

If holding for a gathering, keep the strained cider at 140°F or warmer and verify with a thermometer. Otherwise refrigerate promptly in smaller covered containers, within 2 hours, and use within 3 days or the original cider’s earlier use-by limit. Reheat only the portion needed until steaming hot; cool before sipping.