Put 2 cups cream, half-and-half or milk, the sugar and salt in a saucepan over medium-low heat. If using a vanilla bean, split in half lengthwise and scrape seeds into liquid, then add pod. Cook until mixture begins to steam.
In a bowl, blend cornstarch and remaining cream, half-and-half or milk; there should be no lumps. Remove bean pod from pot and discard. Add cornstarch mixture to pot. Cook, stirring, until it starts to thicken and barely reaches a boil, about 5 minutes. Immediately reduce heat to very low and stir for 5 minutes or so until thick. Stir in vanilla extract, if using.
If mixture has lumps, strain it into a bowl. Chill until cool, a couple of hours (you can skip this step if you have a machine with a built-in freezer). When cool or if there are no lumps, pour into an ice cream machine and freeze according to the manufacturer's instructions.
Honey-Jam Variation: Substitute honey for half the sugar. Add 1/2 cup good jam to mixture before freezing.
Buttermilk or Yogurt: Substitute buttermilk or yogurt for half the cream or milk.
Cherry-Vanilla: Add 1 cup halved, pitted cherries just before freezing.
Strawberry, Blueberry or Peach: Add 1 cup hulled, sliced strawberries, blueberries, or peeled and chopped peaches before freezing.
Coffee: Substitute 1/2 cup very strong coffee for 1/2 cup cream or milk.
Coconut: Substitute 1 cup coconut milk for 1 cup cream or milk; add 1/2 cup toasted dried coconut if you like.
Mint Chocolate Chip: Add 1/2 cup minced mint and 1/2 cup chopped dark chocolate just before freezing.