Sift the flour and set 2/5 cup (100 g) of it aside. To the rest, add the dry yeast, sugar and mix. Make a well in the middle, add the warmed milk, salt, eggs, vanilla and rum flavoring. Gradually knead a smooth dough, adding the flour you had set aside and the melted butter at the end.
Knead until you get a soft and smooth dough. Cover it with a towel and let it rise. Roll it out into a sheet with a thickness of 1/2″ (1.5 cm), and cut out circles with a glass.
Arrange the circles on a floured surface and leave them to rise, covered. Heat oil and fry the donuts on both sides. Fry on a low temperature so the donuts don't end up raw on the inside.