In a mixing bowl, beat the sugar and salt into the egg yolks until thickened and pale yellow. Set aside.
Bring the half-and-half to a simmer in a heavy medium sauce pan or in the top of a double boiler.
Slowly beat the hot half-and-half into the egg mixture. Pour the entire mixture back into the pan saucepan (or double boiler) and stir constantly with a whisk or wooden spoon until the custard thickens slightly. It will not be thick like pudding, it will be more like a thin gravy and will coat the back of the spoon. Be careful not to let the mixture boil or the eggs will scramble.
Remove from the heat and pour the hot custard through a strainer into a large, clean bowl. Allow the custard to cool slightly, then stir in the cream and vanilla. Cover and refrigerate until cold or overnight.
Stir the chilled custard, then freeze in 1 or 2 batches in your ice cream machine according to the manufacturer’s instructions. When finished, the ice cream will be soft but ready to eat. For firmer ice cream, transfer to a freezer-safe container and freeze at least 2 hours.