Add the milk, sugar, and vanilla to a medium saucepan and place on the stove over medium heat.
Stir occasionally until the sugar has dissolved, about five minutes. Then, stir in the baking soda.
Bring to a gentle simmer (don't let it boil over) and reduce the heat to low.
Continue to cook, stirring occasionally, for 1 ½ to 2 hours. Over time, the mixture will darken and become thicker. Stir more frequently in the last twenty minutes to avoid any burning and skim off any foam from the top.
Remove from heat when the mixture is a dark caramel color and has reduced to about a cup.
Let cool slightly and transfer to a jar with a tight lid.
Store in the refrigerator for up to four weeks.