Beat egg yolks in large bowl. Add milk and stir well, then add honey and salt. Pour mixture into top of double boiler and stir constantly over medium heat until it coats back of a spoon. Turn back into bowl, cover, and chill until cold. Stir in berries, cream, and lime juice. Freeze in an ice cream freezer according to manufacturer?s directions. Makes 2 1/2 quarts.