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.