Combine milk and sugar in a wide-based non-stick pan. Whisk constantly to dissolve sugar over medium heat. Visually note the level of milk in the pan.
As soon as the milk boils, reduce heat to a level when it simmers lightly and doesn't over-flow. Let it simmer on medium-low heat for about 20 minutes. Stir at intervals to check.
Then reduce heat to lowest and cook further until the milk has reduced to half and has a thin syrupy consistency, remove from heat and stir the butter. Condensed milk is ready. (It will thicken upon cooling.)
Strain the sweetened condensed milk directly into a clean glass jar to remove any caramel bits. Let it cool.
Store homemade condensed milk in the refrigerator.
Notes
Milk: Try these two alternatives to substitute milk.Evaporated milk: You can replace three cups of milk with 1 can evaporated milk. The cooking will be very little.Coconut milk: You substitute 3 cups of milk with 1 can of coconut cream. Similar to evaporated milk cooking time will be about 5-7 minutes.
Sugar: Replace sugar with 1¼ cup maple syrup or 1 cup honey. Cooking time for maple syrup will increase.
Color: The quality of milk can vary the thickness and color of sweetened condensed milk.
Storage: Store sweetened condensed milk in the fridge and it stays good for more than 7 days. If the top of condensed milk gets crumbly in the fridge, keep it in room temperature and give it a stir and it will be smooth and runny again.