In a medium saucepan, combine half of the strawberries with the sugar and 1/3 cup of water and bring to a simmer. Cook over moderate heat, stirring occasionally, until the sugar is dissolved and the liquid is slightly thickened, about 5 minutes. Transfer the strawberry mixture to a food processor. Add the remaining strawberries and puree until smooth.
Strain the puree through a fine sieve set over a large bowl. Add the Champagne and lemon juice and mix well. Pour the mixture into a 9-by-13-inch glass or stainless steel baking dish.
Freeze the granita for 2 hours. Scrape the frozen edges into the center. Freeze for another 3 hours, scraping hourly, until the granita is icy and flaky. Freeze for 8 hours or overnight. Scrape the granita into bowls and serve.
The granita can be frozen for 4 days.
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