Combine cream, coconut milk, reserved syrup, egg yolks and sugar in a 1 1/2 - 2-quart saucepan. Cook gently over low-medium heat, stirring, until thickened and mixture coats the back of a wooden spoon. Stir in vanilla extract and remove from heat. Strain mixture into a metal bowl and chill, covered, for at least 4 hours or overnight. To freeze, follow ice cream machine’s manufacturer directions, adding chopped lychee when ice cream is almost frozen. Transfer to a container and freeze until serving time.