In a small saucepan over medium-high heat, add the water and sugar and bring to a boil, stirring to dissolve the sugar. Remove from the heat, add the basil, and let cool. Strain out the basil and refrigerate until ready to use. Syrup will last up to 2 weeks in a sealed container in the refrigerator.
Slice 1/4-inch thick slice from the center of the orange. Slice that into quarters and set aside for garnish. Squeeze the juice from the 2 remaining halves into a bowl.
Pour 1 tablespoon orange juice and 1 tablespoon basil simple syrup into a champagne flute. For a mocktail, top with sparkling water. For a cocktail, add about 1/2 cup prosecco per glass and a splash of sparkling water. Garnish with a slice of orange and a basil leaf.