Put the condensed milk, butter, cream, and corn syrup in a 3-quart heavy-duty saucepan and bring to a boil over medium heat, whisking constantly. Add the chocolate and cocoa powder and continue to whisk, making sure there are no pockets of cocoa powder. As soon as the mixture comes back to a boil, turn the heat to medium low and cook, whisking constantly, until the mixture thickens and pulls together into a dense, fudgy batter, about 8 minutes. When the mixture is ready, the whisk will leave trails in the batter, allowing you to briefly see the pan bottom, and when you tilt the pan, the mixture should slide to the side in a blob, leaving a thick residue on the bottom of the pan.
Slide the mixture into a bowl. (Don’t scrape the pan—you don’t want to use any of the batter stuck to the bottom.) Let the mixture cool to room temperature and then refrigerate uncovered until very firm, 3 to 4 hours.
Put the sprinkles in a bowl. Using a teaspoon or a melon baller, scoop the mixture by the teaspoonful, and with your hands, roll each into a ball about 1 inch in diameter. Drop each ball into the sprinkles as you finish rolling it. When you have 4 to 6 brigadeiros, toss them in the sprinkles to coat. You may need to exert a little pressure to ensure that the sprinkles stick.
Store brigadeiros in a tightly covered container at room temperature for up to two days or in the refrigerator for up to two weeks. (If refrigerating, bring to room temperature before serving for the best flavor and texture.)