In a heavy-bottomed pot on medium-low heat, combine goat milk, vanilla extract, cinnamon stick, and sugar. Simmer and stir periodically with a wooden spoon until sugar is dissolved, about ten minutes. Be sure to scrape the bottom of the pot well so that no sugar sticks. Tip: Choose a pot that is larger than you think you'll need just in case the mixture starts to bubble up. You don't want to clean burnt sugar off of the stove top.
Dissolve baking soda in water and add to milk/sugar mixture. This helps prevent lumps and aids in caramelizing.
Reduce heat to low and cook for three hours, stirring periodically, or until the mixture has thickened and coats the back of a spoon. The volume should be roughly 1/4 of what you started with. Note that as the volume decreases, the mixture will come to more of a boil and you'll need to stir more often. For the last half hour, I recommend stirring constantly.
Remove from heat and discard the cinnamon stick. Cool and transfer to jars and refrigerate.
Notes
The total yield is two cups, which will fill four half-pint jars.Keep cajeta refrigerated until you're ready to use it. It should last for several months.This recipe is a modified version of the one from Coco Cooks.