For the dough: Combine milk, yeast and sugar, let soak for about 10 minutes. Place flour, salt, rum flavor, egg and butter in a bowl. Pour yeast mixture into bowl and knead into a smooth dough. Add more flour or milk as needed. Covered and let rise in a warm place for about 1 hour.
Grease a pan with butter. Preheat the oven to 200°C (approximately 400°F).
Melt butter in a pot and let cool slightly. Combine sugar and cinnamon. Divide dough into 4-5 pieces and roll on a lightly floured surface into strands. Cut the strands into small pieces. Roll pieces into balls and dredge balls in butter, then cinnamon-sugar. Place balls in the pan and bake for about 35 minutes. Remove, let cool for about 30 minutes, then flip onto a plate. Serve warm.