Stir together the milk and sugar in a medium sauce pan. Add the cinnamon stick, baking soda, and vanilla.
Bring just to a boil, stirring frequently to dissolve the sugar, and then immediately reduce the heat to a simmer.
Simmer uncovered for 1 ½ to 2 hours, stirring occasionally, until you've reached your desired color. Remove the cinnamon stick and pour the cajeta into heat-safe jars. Store in the refrigerator.
