Bring the juice of 5 lemons and 3/4 cup each sugar and water to a boil. Add 1/2 cup basil leaves and the zest of 2 lemons (in wide strips) and steep, off the heat, 45 minutes; strain. Add 2 cups cold water, then pour into a baking dish and freeze 1 hour. Meanwhile, hollow out 6 of the juiced lemon halves and freeze. Scrape the ice with a fork; freeze 4 more hours, scraping every hour. Serve in the lemon cups.