Melt the butter in a saucepan over low heat, add the cocoa powder and sweetened condensed milk, and stir continuously until the mixture has reached a thick, gooey consistency. Spread the mixture over a flat plate and refrigerate for 3 hours.
Peel the carrots, chop them into smaller pieces, and place them in a blender. Add the eggs and vegetable oil to the blender and puree the mixture until smooth.
Pour the smooth mixture into a bowl and combine with the flour, sugar, and baking powder.
Form 17 chocolate fudge balls from the chilled brigadeiro mixture and roll them in flour.
Pour the carrot cake mixture into a greased tube pan and let the flour-coated brigadeiros sink into the batter. Transfer the tube pan to a preheated oven, cook at 350°F for 1 hour, and then let cool for 1 hour.
For the chocolate glaze, add the sugar, cocoa powder, milk, and butter to a saucepan over low heat and bring to a boil. Once the butter has melted and the sugar has completely dissolved, remove the saucepan from the heat and let cool for 1 hour. Pour the chocolate glaze over the Brazilian carrot cake and top with chocolate sprinkles before serving.
