Combine 1 1/2 cups cherries and sugar in a small saucepan; let stand 10 minutes or until juices have released, stirring occasionally. Place pan over medium-high. Add 1 cup water, 6 basil sprigs, and ginger to pan; bring to a boil. Cook 10 minutes or until sugar dissolves and cherries have broken down. Remove pan from heat. Gently mash cherry mixture with a potato masher or a fork. Let stand 30 minutes at room temperature.
Strain cherry mixture through a mesh sieve over a large pitcher; discard solids. Add remaining 3 cups water, lemon juice, and vodka to pitcher; stir gently to combine. Stir in remaining 1/2 cup fresh cherries. Add seltzer water to pitcher just before serving. Pour about 1 cup cherry mixture into each of 8 ice-filled glasses. Garnish each glass with a small basil sprig.