In a large saucepan, bring 3 cups strawberries, sugar, and ¼ cup basil leaves to a boil over medium-high heat, using the back of a spoon to mash berries. Cook until slightly thickened, about 5 minutes. Strain through a fine-mesh sieve, discarding pulp and basil. Refrigerate until chilled.

In a large pitcher, stir together strawberry-basil syrup, seltzer water, lime juice, orange zest, remaining 3 cups strawberries, and remaining ½ cup basil leaves. Add ice to serve.