In a small metal bowl you will need to combine yeast, warm water, and 1 teaspoon sugar.
Set aside until foamy this will take about 10 minutes. While this is happening set up your stations. You will need a pan for the oil, drying rack, and a place to dust the doughnuts if you want. I chose not to add more sugar to mine.
Place flour in a large bowl. Then make a hole in the middle of the flour. You will then add in the eggs/ yeast mixture. The 1/4 cup sugar, butter, nutmeg, and salt. I love these measuring spoons by utensi.
Using a wooden spoon, stir until a sticky dough forms. Then this is when you put them on a well-floured surface. You will knead the dough until it smooth and has a rubber-like feel.
Place in an oiled bowl; cover with plastic wrap. Set in a warm place to rise until doubled, 1 to 1 1/2 hours.
On a lightly floured work surface, roll dough to 1/4-inch thickness.
I then make balls that are the same size. If you want to go for a more uniformed look you can use a 2 1/2-inch-round cutter or drinking glass.
Cover with plastic wrap; let rise 15 minutes.
In medium saucepan over medium heat, heat oil until a deep-frying thermometer registers 370 degrees.
Using a slotted spoon, carefully flip the doughnut into the oil.
Fry until golden it takes about 40 seconds.
Turn doughnuts over; fry until golden on other side, another 40 seconds.
Using a slotted spoon, transfer to a paper-towel-lined baking sheet or the baking rack with a paper towel under it or a cookie sheet to catch the grease.
Roll in sugar while warm. I usually do not add more sugar but you can if you want to do so.
Fill a pastry bag fitted with a #4 tip with jam. If you do not have one use a plastic ziplock bag and cut a hole in the tip of the bag. I used these icing tip set and bags.
Using a wooden skewer or toothpick or the end of the thermometer you checked the oil with.
Then make a hole in the side of each doughnut.
Fit the pastry tip into a hole and pipe about 2 teaspoons jam into doughnut.