Place the vanilla bean, 3 cups of the milk, the sugar, water, and baking soda in the insert of the slow cooker, and whisk them together. Cook for 9 hours on HIGH, uncovered, then remove the vanilla bean and whisk the milk mixture gently. Use a dull-edged butter knife to carefully scrape down the crust of sugar that accumulates on the sides of the insert. Do not skim the foam off the top of the mixture.

Continue cooking for 1 more hour, stirring every 20 minutes, until it is a rich medium-caramel color and has thickened to the consistency of melted ice cream. In the meantime, warm the remaining 1 cup of milk in a small saucepan. Turn off the slow cooker, and stir in the warm milk. (This will prevent the dulce de leche from hardening while refrigerated.) Carefully remove the insert. Allow the mixture to cool for 10 minutes, then spoon and scrape it into a small metal bowl. Cover and cool to room temperature. The mixture will thicken slightly as it cools. Refrigerate it in a tightly covered container for up to 3 months.