Sift flour into a bowl (or bowl of your stand mixer) and set aside. Warm milk on the stove or in a microwave until it’s warm, but not hot, to the touch. Stir in one teaspoon of sugar and all of the yeast. Set aside until the yeast gets bubbly.
Meanwhile take another bowl and whisk together reaming sugar with egg yolks, egg, butter, vanilla, rum, salt and lemon zest. Stir the yeast mixture into the flour slowly, then pour in the egg mixture and knead dough with a dough hook for a few minutes until the dough comes together and pulls away from the sides.
The dough will be somewhat sticky, but it should be smooth with no patches of flour visible. Give it a light knead, just a few minutes, with your hands then transfer it to a large oiled bowl. Cover loosely with plastic wrap and transfer to the refrigerator. Let proof overnight.
Shape doughnuts
The next day, take the dough out of the refrigerator. Let it rest for 10 minutes at room temperature. Then remove it from the bowl and place it on a lightly floured work surface.
Slice dough into 12 equal pieces (each should weigh between 2.5-3 ounces or 70-80g). Shape each piece into a ball and place it on a piece of parchment paper (or silpat) dusted with flour. Leave enough room between all the dough balls, as they will rise. Cover the doughnuts with a light kitchen towel (or plastic wrap) and let rise until doubled in size, about 2 hours.