Pre-heat a grill or grill pan over high heat. When hot, add the orange rounds, and grill for about 1 minute on each side until some nice grill marks appear. Transfer to a wire rack and let cool completely. Leave half of the rounds intact, and slice the rest in half.
In a pitcher, combine the Campari, bourbon and orange juice. Add half of the cooled orange rounds. (At this point, you can pop the punch into the fridge until ready to serve.)
When ready to serve, add the club soda and ice to the pitcher OR pour the punch into glasses with ice and top each with soda to taste.
Garnish each glass with a grilled orange half (or two) and drink up!