In a medium nonstick saucepan, combine the condensed milk with the white chocolate and 1 teaspoon of butter. Cook over moderately low heat, stirring constantly, until shiny and very thick, 15 to 18 minutes.
Spread the mixture in a shallow dish and let cool for 15 minutes.
Arrange 30 paper candy cups on a baking sheet. In a shallow bowl, mix the pecans with the cinnamon. Rub your hands with butter. Scoop up rounded teaspoons of the candy mixture and roll them into balls.
Roll the candy in the pecan mixture and set them in a paper cup. Repeat to form the remaining candies.
