Place one orange half slice, 1 cherry, 2 dashes bitters, and ½ teaspoon sugar in each of two rocks glasses. Muddle until the fruit is well mashed (see Note).
Fill each of the two glasses with ice, add the bourbon or other spirit, and stir well. Top off each glass with 2 ounces club soda and stir well. Garnish each glass with the remaining orange slice and cherry, one in each drink.
Notes
To muddle, place the oranges, cherries, bitters and sugar in the bottom of a cocktail shaker, or a sturdy glass. Use the flat end of the muddle to press the fruit, twisting as you go. You’re aiming to crush and break down the fruit to release as much juice and oils from the produce as possible.