For the Dulce de Leche: 

• In a large stockpot, whisk together the milk, sugar, vanilla, baking soda, and salt and bring to a boil over medium heat, which should take 12 to 15 minutes. Once the mixture reaches a boil, reduce the heat to medium-low and set a timer for 45 minutes. At this point, you’ll need to babysit the sauce for the next 10 minutes and whisk often to prevent it from foaming over as moisture evaporates.
• Let the dulce de leche simmer over medium-low for a total of 40 to 45 minutes, stirring occasionally. Keep in mind that the sauce will thicken as it cools, so don’t cook it past 45 minutes, or you’ll end up with hard candy.
• Let the dulce de leche cool completely, then strain and transfer to a jar and refrigerate overnight for the flavors to develop further. Dulce de leche should be stored in an airtight jar or container in the refrigerator, and will keep for 3 to 4 weeks if stored properly.

For the Churros: 

• In a medium sized saucepan combine the water, milk, butter, and salt and cook over medium heat until butter has melted and the mixture just starts to simmer.
• Leave the heat on and add all the flour and stir until the mixture is combined and starts to form a ball. Cook for a minute or so more, until the dough firms up just a little bit more and starts to leave a slight film on the bottom of the pan.
• Transfer the dough to a large bowl and let cool for 5 minutes. After 5 minutes add the eggs, one at a time, stirring very well to make sure each egg is mixed in before adding the next. After all the eggs have been added, transfer the dough to a piping bag fitted with a Wilton 1M Piping tip.
• Set the dough aside to rest while you heat up 3-4 inches of oil in a large dutch oven to 3600-3750.
• Once the oil’s hot, pipe the churros out in 5-6″ lengths and cut with a pair of scissors into the oil. Cook for 1-2 minutes on the first side then flip and cook for 1 more minute.
• Transfer the churros to a paper towel lined plate to cool for about a minute then toss in the cinnamon sugar and serve with the Dulce de leche.