In a small bowl, mix together 1/4 cup of goats milk with the baking soda. Set aside.
Place the remaining goats milk, sugar, and cinnamon stick in a large Dutch oven or pot over medium to medium-high heat. Bring the mixture to a simmer, stirring frequently to dissolve the sugar.
Remove the pot from the heat and add in the baking soda mixture. The milk will begin to bubble and froth up quickly. Continue stirring. Once the mixture stops bubbling, return the pot to the heat and bring it back to a low simmer.
Cook until the mixture has reduced and thickened (about 45-60 minutes). Be sure to stir frequently, especially towards the end of the cooking time, scraping the bottom of the pot so it doesn't burn. The cajeta is done when you can scrape the mixture aside and see the bottom of the pot.* It should be thick like honey.
Remove the pot from the heat and stir in the vanilla extract.
Notes
For a thinner consistency, stop cooking the cajeta when it's thick enough to coat the back of a spoon, and only momentarily leaves an empty trail whenever you scrape the bottom of the pot with a spatula.
For a thicker consistency, stop cooking the cajeta when you can scrape the bottom of the pot with a spatula and it easily leaves an empty trail for a few seconds. You'll know when it reaches this point because the cajeta will be undeniably thick!
Cajeta will thicken once it cools. To soften it, heat it up in the microwave a few seconds at a time or run it under hot water.