Begin by slicing the orange and halving the lemon. In a large pot or slow cooker, combine the apple cider with the sliced orange, halved lemon, cinnamon sticks, whole cloves, star anise, and brown sugar. I like to smell all the spices together first to make sure they're balanced, adjusting slightly if one scent seems too strong.
If using a pot, heat the mixture over medium-high heat until it just begins to bubble gently, then reduce the heat to low, cover, and simmer for at least 30 minutes. For a slow cooker, set it to low heat and allow the cider to warm and infuse for 2-2.5 hours. Longer infusion times at a gentle heat really allow the spices to blossom.
After the simmering period, carefully taste the mulled cider. Adjust the sweetness if needed by stirring in additional brown sugar until it reaches your desired flavor profile. I always taste before serving, sometimes a little extra sweetness balances the spices perfectly. Serve the warm cider immediately, garnished with fresh orange slices and star anise from the pot, or fresh ones if desired.