In a small bowl, mix together 2 tbsp goat milk with the baking soda. Set aside.
In a large heavy-bottomed pot over medium heat, stir the remaining goat milk, sugar, cinnamon stick, and salt. Stir frequently until the sugar has dissolved and it reaches a simmer*(see notes). The milk will look foamy at this stage.
Once simmering, remove from the heat and stir in the baking soda mixture. Be sure to scrape out all the baking soda into the milk.
Return the pot to the stove and reduce to medium-low heat. Continue to simmer the mixture for 1 hour 15 minutes, stirring frequently until it has reduced and thickened. Be sure to scrape the bottom and sides of the pot to prevent the caramel from burning. It will start to brown after about 20 minutes. You'll know it's done when the caramel thoroughly coats the back of a spoon.
Remove from the heat and stir in the vanilla extract. Remove the cinnamon stick and discard it.
Place it into an airtight container and cool to room temperature before storing in the fridge.
Notes
Simmering the milk: Keep a very close eye on the milk as it reaches a simmer. It doesn't take long for it to go from simmering to boiling, and when it boils, it could easily spill over onto the stove.
Use a pot that's big enough to allow the caramel to bubble up when you add the baking soda.
The cajeta will last up to 1 month in the fridge when stored in an airtight container.