In a medium mixing bowl, whisk 1 1/2 cup flour (reserve extra for dusting the table top later), baking powder, 1/4 tsp. salt, and nutmeg. In a second medium bowl, whisk liquid eggs and half of sugar (reserving half for topping) until it turns pale yellow, about 1 minute.. Add vanilla extract and whisk 1 more minute.

In a microwave or small pot, melt butter and add milk to butter. Combine the mixtures in stages: first, add 1/3 flour-nutmeg mix and 1/2 butter-milk mix to egg-sugar mix and stir to combine. Again, add 1/3 flour-nutmeg mix and 1/2 butter-milk mix and stir to combine. Finally, add remaining flour-nutmeg mix and stir to combine. Mix until dough is smooth and free of lumps. Cover with plastic and let rest at room temperature for 30 minutes.

Start heating oil on medium-high heat in a small pot; it will take approximately 15-17 minutes to reach temperature. (If you have a candy thermometer, you want heat between 360-375 degrees) Lightly dust your work surface with reserved flour and turn dough onto table. Lightly dust dough with flour. If dough is too sticky, dust with more flour. Roll dough out to about 1/4" thick and use round cutters or a cup to cut into circles. (Optimal size for the cup or cutters is 3": should result in 6 doughnuts and 6 doughnut holes.) To make the center hole, use a smaller cutter or a bottle top or anything you can find! You can re-roll dough if you make a mistake; however, the more times you roll, the tougher the dough will get.

Test oil temperature by adding a pinch of batter to it. It should sizzle gently. If it browns immediately, turn the heat down and let the oil cool. If it doesn't brown, increase the heat. Keep heat in between medium and high. Fry one round doughnut and one hole at a time, about 1 minute on each side. Adjust oil temperature as needed. (Be very careful when flipping the doughnuts: oil is very hot! Use heat-safe tongs, a metal spatula, slotted spoon, or chop sticks to handle doughnuts in and out of the oil.)

In a mixing bowl, add remaining sugar and cinnamon and mix thoroughly. Remove doughnuts from oil when both sides are golden and transfer them to a paper towel-lined baking sheet or a brown paper bag to help soak up the oil. Let doughnuts cool for about a minute and then toss in cinnamon/sugar mixture.

Let cool or eat warm! Enjoy!