Make simple syrup: Combine the sugar and 1 cup water in a saucepan over medium-low heat, stirring until the sugar dissolves.
Bring 1 cup of the simple syrup, the juice and wine to a boil in a saucepan over high heat. Carefully transfer to a blender, add the basil and pulse until smooth (leave the filler cap off to let steam escape). Strain through a fine-mesh sieve into an 8-inch square metal pan. Freeze 3 to 4 hours, scraping the mixture with a fork every 20 minutes to make it slushy; freeze until ready to serve.
Cut off the tops of the strawberries and trim the bottoms so that they sit upright. Using a small melon baller, scoop out the inside of each strawberry to make a small cup. Fill with a spoonful of the granita.