In a large, heavy-bottomed saucepan, combine the whole milk and granulated sugar over medium heat. Stir constantly with a wooden spoon or heatproof spatula until the sugar is completely dissolved.

Once the sugar has dissolved, stir in the baking soda. The mixture will bubble up and foam slightly, which is a normal reaction that helps give the caramel its smooth texture and rich color.

Reduce the heat to medium-low and bring the mixture to a gentle, steady simmer. Allow it to cook uncovered, stirring occasionally, for about 1 hour as it begins to reduce and take on a pale golden hue.

After the first hour, keep a closer eye on the pan and stir more frequently to prevent the sugars from burning at the bottom. The milk will continue to thicken and deepen into a rich amber color over the next 45 to 60 minutes.

When the mixture heavily coats the back of a spoon and leaves a clear path when you drag your finger through it, remove the pan from the heat. Carefully stir in the vanilla extract and a pinch of sea salt to balance the sweetness.

Transfer the hot dulce de leche to a heatproof glass jar and let it cool completely at room temperature, keeping in mind it will thicken significantly as it cools. Serve drizzled over warm brownies or store in the refrigerator for up to 3 weeks.