In a medium saucepan over low to medium heat, combine the sweetened condensed milk, 1 cup of shredded coconut, and butter.
Stir until the butter melts and all ingredients are combined into a smooth mixture. Continue to stir constantly. The mixture should begin to thicken. Cook for about 10-15 minutes, or until the mixture is thick enough to pull away from the bottom of the pan and creates a trail that does not immediately close when you run the spatula through it.
When the mixture reaches the right consistency, remove it from the heat. Transfer it to a buttered plate and let it cool at room temperature for about 15-20 minutes, or until it is firm enough to handle.
Grease your hands with a little butter to prevent the mixture from sticking. Scoop a tablespoon of the mixture and roll it into a small ball about 2 cm in diameter.
Place the ½ cup of shredded coconut in a bowl. Roll the balls in the coconut until they are completely coated. Place the finished Beijinho in small paper cups.