Place milk in a small saucepan on the stove and heat until bubbles appear all around the sides of the pan. Remove milk and let cool until it’s lukewarm.
While the milk is cooling, combine the yeast with the warm water and a pinch of sugar in a small bowl or glass measuring cup. Stir and let sit for five minutes — after five minutes, it should look almost creamy. That’s a sign the yeast works!
Place the yeast/water, warm milk, sugar, salt, nutmeg, flour, eggs and 2 tbsp oil in a large bowl of a stand mixer. Beat with a paddle attachment until dough forms and then switch to the dough attachment and continue mixing on high speed for five minutes and until the dough pulls away from the sides. If you don’t have a dough attachment, stick with the paddle. If you don’t have a stand mixer, knead by hand for 8-10 minutes until a smooth dough forms.
The dough should be very smooth and not sticky. If the dough is still sticky, add a bit more flour until the dough is no longer sticky. Place dough in an oiled bowl, cover with a cloth and let rise in a warm spot for 1 hour to 1 1/2 hours or until doubled in size.
After rising, punch the dough down and transfer to a lightly floured work surface. Roll the dough until it’s about 1/4 to 1/2-inch thick. Cut circles of dough using the bottom of a glass jar or a biscuit cutter (about 3-inches round).
Place the circles of dough evenly onto a sheet pan lined with parchment paper. Place about two teaspoons of jam in the center of one circle of dough. Place another circle of dough on top and FIRMLY SEAL EDGES TOGETHER! If you don’t crimp the edges to seal well enough, they will open up while frying. Repeat until you have used all of the dough.
Cover donuts loosely with plastic wrap or a kitchen towel and let rise for about 30 minutes while you are heating the oil.
While donuts rise, heat up the rest of the vegetable oil in a large heavy pot over medium/high heat. Use a candy thermometer to check the temperature of the oil — it should register at about 375 degrees F when ready for frying. If it’s too hot it will burn the donuts and if it’s too cool, the dough will absorb extra oil and take a longer time to fry.
When the oil is ready, carefully and gently drop in two donuts at a time. They should sizzle and little bubbles should instantly appear all around the edges of the donut. Fry for about five minutes per side. Flip donuts carefully in the oil using tongs, a spatula or big spoon.
Donuts are done when they are a deep golden brown color. You want the color to be brown — too light and they won’t be cooked through on the inside. Remove the donuts with a slotted spoon or spatula and place on paper towels to drain.
Repeat with remaining donuts until all are fried.
Let them cool briefly, then sift powdered sugar over tops. Or while they are still warm, gently toss in granulated sugar. Enjoy warm!