Combine 2 cups blood-orange juice and spices in a saucepan and bring to a boil over medium-high heat. Remove from heat and let cool. Transfer to a container, cover, and refrigerate at least 12 hours and up to 1 day. Pour mulled juice through a fine sieve into a punch bowl; discard spices. Stir remaining 2 cups blood-orange juice and regular orange juice into mulled mixture and garnish with orange rounds. Serve as is or topped with sparkling wine, sparkling water, or vodka.