Stir milk, sugar and baking soda together in a large, heavy-bottomed pan.

Bring the mixture to a gentle boil and then reduce heat and let simmer for 2 hours. Stir occasionally, but watch closely. The liquid will thicken and reduce in volume.

As the mixture starts to brown and become thicker, you'll have to stir more frequently to prevent it from burning/sticking to the bottom of the pan.

Once the doce de leite has reached the color and consistency that you like, stir in the vanilla extract and turn the burner off.

Let it cool slightly and transfer to a jar with a lid. The doce de leite can be served immediately. It will continue to thicken as it cools.

Uncover the dish and whisk the doce de leite until it's smooth.

Preheat the oven to 450°F.

Open the can of condensed milk and pour it into a shallow baking dish. Cover the baking dish with foil and place the dish in a large roasting pan.

Fill the roasting pan with boiling water until it reaches half-way up the side of the baking dish. Bake in the oven for 1 hour and 45 mins.

Let the roasting pan cool slightly and then remove the baking dish from the water bath

Heat ½ cup sugar over medium heat in a non-stick frying pan or 2-quart saucepan. Stir constantly using a rubber spatula. Within a few minutes the sugar will start to liquify and turn amber in color. Keep stirring until the sugar fully dissolves into a brown-colored syrup.

Turn the flame down to the lowest setting and add the butter and baking soda at the same time. Then add sweetened condensed milk and keep stirring. The caramelized sugar will start to harden, keep stirring and the mixture will become smooth again after 5-7 minutes. 

Once the mixture is completely smooth, carefully transfer it to a small bowl or jar with lid. Serve while it's still warm.