In a medium sized sauce pan, heat water and sugar over medium-high heat until sugar is dissolved. Remove from the heat and let cool. Once the sugar water solution has cooled, transfer to a loaf pan or 8 x 8 pan. Freeze for 2 hours.
After two hours, remove pan from freezer and scrape with a fork to form ice crystals. Return to freezer and continue to freeze and scrape every 2 hours until frozen through.
In a small sauce pan, combine blackberries, sugar, lime juice, and lime zest. Heat berry sauce over medium heat, stirring often with a wooden spoon. Continue to cook until sauce comes to a simmer, let simmer for one minute. Remove from heat, stir in torn basil leaves, and let steep for 10 minutes.
Pour blackberry sauce through a fine mesh strainer and transfer into a small bowl or jar. Refrigerate until chilled.
When ready to serve, make basil sugar by combining 1 TB finely chopped basil with 1 TB sugar. Remove shaved ice from freezer and scrape again using a fork. Scoop ice into individual bowls and pour blackberry sauce over shaved ice using a spoon or jar with a pour spout (add water to syrup, one tsp at a time, to reach desired pouring consistency, if needed). Top with basil sugar and garnish with basil leaves and blackberries.
Recipe by at https://www.adventuregathereat.com/blackberry-basil-shaved-ice/