Pour the cranberry juice into a saucepan and place over low heat, warming gently until just steaming, about 3-4 minutes, filling your space with a fruity aroma.
Add the cinnamon stick and cloves to the warm juice, allowing them to simmer gently for 10 minutes to infuse the flavors and aromas, which will deepen the ruby color of the mixture.
Meanwhile, use a muddler to crush the orange slices in a cocktail shaker, releasing their oils and zest, and add a splash of bourbon for a zesty, boozy kick. Stir gently to combine.
Once the spice-infused juice is fragrant and hot (but not boiling), remove the cinnamon and cloves with a strainer to prevent over-extraction.
Pour the warm, spiced cranberry juice through a strainer into mugs, filling each about three-quarters full to leave room for the bourbon mixture.
Top each mug with the muddled orange and bourbon mixture, stirring gently to combine all the flavors and release the citrus oils into the warm drink.
Garnish each mug with a sprig of fresh rosemary and a cinnamon stick, enhancing the festive aroma and presentation.
Serve immediately while steaming and fragrant, allowing everyone to enjoy the comforting blend of spice, citrus, and warmth.