Pour the milk into a pan over moderate heat and whisk in the egg yolk. Stir in the vanilla rennet and remove from the heat and pour into a large bowl to set for about 10 minutes. When it starts to set, place in the refrigerator to chill. Pour the cold water into a saucepan over moderate heat and add both the sugars. Stir to dissolve and add the cinnamon stick. Mixture should clear in about 8 minutes.
Remove the set junket from the refrigerator and place on low heat. Very slowly, a little at a time, pour in the cinnamon-flavored syrup with the cinnamon stick. This will separate the rennet into little pieces. Cook for 1 1/2 hours over low heat. When cooked, (it will curd tightly), remove from the heat and allow to cool. Place in the refrigerator to thoroughly chill, ice cold in fact.
Serve in bowls.