In Dutch oven, stir 2 tablespoons of the sugar over medium heat with a wooden spoon until melted and lightly browned, 2 to 3 minutes. Stir in milk, 3 cups sugar, vanilla, and baking soda. The browned sugar will immediately harden but will dissolve again as you continue to stir.
Increase the heat to high and bring the mixture to a boil. Simmer for 1 minute, then reduce the heat to low. Cook for 2 hours, stirring intermittently. The mixture should reduce to almost half.
Increase the heat to medium and maintain a low simmer, stirring frequently. Cook until the caramel thickens and begins to foam slightly, another 45 to 50 minutes. The caramel is done when it turns a light golden brown and easily coats the back of a spoon.
Remove from the heat and pour into a clean glass or ceramic container. Cool completely and refrigerate until ready to use (it will keep for 2 to 3 weeks). The caramel has a thicker consistency when cold.