Massage the basil leaves to release flavor and place them in a pitcher. Squeeze the juice of 3 limes into the pitcher. Discard lime rinds. Add the strawberry simple syrup, rum and seltzer. Stir to combine. Add strawberries. Allow the mixture to sit for at least 10 minutes before serving.
To serve, place ice into four highball glasses. Pour the strawberry mojito mixture over ice and garnish with lime wedges from the remaining lime.
Strawberry Simple Syrup
Combine water, sugar and strawberries in a medium pot and bring to a boil over medium-high heat. Once boiling, remove the pot from the heat and cover. Let the simple syrup come to room temperature (this will take about 30 minutes).
Set a strainer over a bowl and pour in the room temperature simple syrup. Lightly press the strawberries to remove any excess simple syrup. Discard strawberries. You can store the simple syrup in a mason jar in the fridge.