Place the milk, sugar and cinnamon stick in a large, heavy-bottomed saucepan over medium heat. Stir to dissolve the sugar, while heating the milk to a gentle simmer. The milk will begin to form a foamy layer across the surface and around the perimeter of the pan. Stir the mixture gently to incorporate.
Dissolve the baking soda in the water. Stir the baking soda mixture into the milk mixture. Reduce the heat to low and cook the mixture uncovered at a low simmer, just so the milk's surface breaks with a gentle roll.
Check the mixture periodically and gently stir without incorporating the foamy layer that forms across the surface.
After the mixture has been simmering for 1 hour, remove the cinnamon stick. The milk mixture will begin to turn a light tan color. Continue simmering until the mixture reduces to the thickness of sweetened condensed milk, takes on a rich tan color and has reduced to about one cup, about 1 to 1-1/2 additional hours. The mixture will thicken further as it cools and under refrigeration.
Strain the mixture immediately into a jar, using a fine mesh strainer. Cool completely. Refrigerate for up to 3 weeks.
Nutrition analysis per ounce: 170 calories, 4 grams protein, 31 grams carbohydrate, 4 grams fat, 15 milligrams cholesterol, 140 milligrams sodium
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