In a Dutch oven or wide, heavy-bottomed saucepan, combine milk, sugar, baking soda, salt, and cinnamon sticks. Stir over medium heat until sugar dissolves. Increase heat to high and bring to a boil. Simmer for 2 minutes, stir. Reduce heat to low and cook for about 2 hours, stirring intermittently. The mixture should have reduced to almost half.
Increase heat to medium and maintain a low simmer while stirring frequently. Cook another 45 to 50 minutes, until caramel has thickened and begun to foam slightly. Remove cinnamon sticks.
Caramel is done when it turns light golden brown and easily coats back of spoon. Remove from heat and allow to cool 10 minutes. Cool completely and refrigerate until ready to use.