Puree strawberries in a blender or food processor.
In a medium saucepan, combine still water, granulated sugar, strawberry puree, and basil. Bring to a boil over medium-high heat. Lower heat and simmer, stirring occasionally, 5-8 minutes. Remove from heat and cool to room temperature.
Strain cooled mixture through a fine-mesh sieve, pressing to extract juices. Discard solids. Chill syrup until ready to use.
Pour a few tablespoons of strawberry basil syrup into a glass (use more or less, to taste). Fill with ice and sparkling water. Garnish with a sprig of fresh basil and a fresh strawberry slice.
The strawberry-basil syrup will stay fresh for a week or two in the refrigerator in a tightly-sealed container. Stir before using.For more serving ideas, including cocktail inspo for adults, see the Recipe Variations section in the article above.