Combine water and brown sugar in a medium saucepan over high heat. Bring to a boil, reduce heat to medium and let cook until sugar dissolves into a simple syrup. Remove from heat and let cool.
In a blender, combine 2 cups strawberries with basil leaves and 1 tablespoon lemon juice; pulse until blended. Set aside. Repeat with remaining strawberries, basil, and lemon juice. Divide simple syrup evenly among batches.
Pour into popsicle molds and freeze for at least six hours (popsicles will keep in freezer up to 2 weeks).
Place popsicle upside down in a wine glass and pour Prosecco over.
