Place the Florida Strawberries, sugar, and cornstarch in a food processor. Process until smooth.
Pour the strawberry mixture into a saucepan along with 3 tablespoons of water. Bring the mixture to a boil then reduce heat and simmer for 5 minutes while stirring frequently. Remove from heat and cool completely.
When the strawberry mixture is cool divide it into 1/4 cup servings and place in freezer bags, remove all air, and zip them up. You can freeze this strawberry sauce for up to 6 months.
To make the bellini's, place 1-2 teaspoons of thawed strawberry sauce in the bottom of each of 6 champagne flutes. Fill with champagne or sparkling wine.
Make a slit in each of the strawberries and place on the rim of the flute.