Combine the apple cider, orange juice, and lemon juice in a large stockpot or Dutch oven. Stir to mix.
Add the whole spices: cinnamon stick, cloves, and star anise. If using fresh nutmeg, grate it directly into the pot. If using ground nutmeg, add it now.
Add the sliced orange to the pot. These will infuse the liquid with a lovely citrus aroma and flavor.
Place the pot over medium heat. Bring the mixture *just* to a simmer – do not let it boil, as this can dull the flavors. Once simmering, reduce the heat to low, cover, and let it steep for at least 30 minutes, or up to 2 hours for a richer flavor.
If you prefer a sweeter wassail, stir in the brown sugar or maple syrup during the last 15 minutes of simmering, tasting and adjusting as needed.
If making an alcoholic version, stir in your chosen spirit (rum, brandy, or bourbon) just before serving. Gently heat through, but again, avoid boiling.
To serve, carefully ladle the wassail into mugs through a fine-mesh sieve to catch the spices and orange slices. Garnish each mug with a fresh orange slice or a cinnamon stick, if desired.