Split vanilla bean lengthwise and scrape seeds into a bowl, reserving pod for another use. Whisk in sugar, cornstarch, and salt until combined well.
In a saucepan simmer Muscat and 1/8 cup each type of berry 2 minutes. Drain mixture in a sieve set over a bowl, reserving liquid. Transfer cooked berries to a large bowl and stir in remaining fresh berries. Coarsely chop basil.
Gradually whisk reserved hot liquid into sugar mixture until smooth. Transfer mixture to pan and stir in basil. Bring mixture to a boil, whisking, and simmer, whisking, 3 minutes. Immediately pour mixture through sieve into berries, discarding basil, and stir until combined well. Stir in lemon juice. Divide kissel among 6 bowls. Chill kissel, covered, at least 2 hours, or until cold, and up to 2 days.
Serve kissel with creme fraiche or sour cream.