In a small bowl, add warm milk and sprinkle the yeast and the tsp of sugar on top. stir lightly and leave it to the side.
In the mixing bowl of your stand mixer, combine flour, the rest of the sugar, salt, your choice of nutmeg or cinnamon.
By now, the yeast should be blooming, as in, there should be a frothy foam forming in the little bowl.Add all wet ingredients into the milk - eggs, melted butter and vanilla. Mix well. Add the wet ingredients to the dry and mix on low with the dough hook till well combined and the dough is starting to form.
At this point, increase the speed of the mixer to medium (4 on a KitchenAid) and let it kneed the dough for 10 minutes. If you don't have an electric mixer, this is where you need a little elbow grease. Lay the dough out on your clean counters, making sure to not add any flour. the dough will be wet, and a little sticky. Kneed the dough, folding over and pushing it forward, this will take a good 10-15 minutes. This step is a fantastic way to get that arm workout in!In both scenarios, you will know when you are done, because the dough is soft and when poked with your finger the indent will disappear in the dough. If the indent is still visible, keep kneading. once you have kneaded all your frustrations away, lightly oil a bowl, place your dough in, and brush the dough with oil so that no skin forms. Cover with a clean kitchen towel, and place it in a warm dark place.Let the dough rise for 1.5 hours, resist the urge to check. You are looking for the dough to double in volume. After the 1.5 hours, your dough will be fragrant, and have doubled in volume. IT WILL BE GLORIOUS.
Flour your work surface, and dump out your dough on the counter. Now, you can spread the dough out a little and use a rolling pin to roll the dough out to a 1/4 inch thickness.
using a circle cookie cutter/mason jar lid/doughnut cutter, cut out circles then punch out the holes in the enter with the fat end of a piping tip.This dough is soft and pliable, so feel free to collect the extra dough and re-roll more circles.I got 24 doughnuts with a mason jar lid. Lay out all your cut out doughnuts on a cookie sheet covered with parchment, spacing them out a little, cover with a clean kitchen towel and let sit to rise for 30 min.
After the second rise, heat vegetable oil in a pot with high sides to medium - 320 degrees Fahrenheit, it should not be too hot.
add doughnuts to the hot oil 2-3 at a time to let them swim around. Flip once as you see a golden colour forming on the bottom(about 30-45 seconds). Flip, and wait another 30 seconds and pull them out of the oil and rest on a cooling rack.Complete frying all doughnuts.