In a small bowl, stir together the yeast, warm milk, 1 teaspoon sugar, and set aside for it to proof for about 15 minutes. The yeast has proofed successfully if the mixture is foamy and has doubled in size after the wait time.
In a large bowl, pour in the flour and make a well in the center to add in the egg yolks, yeast mixture, ¼ cup sugar, butter, salt, and stir until the dough begins to come together and is sticky to the touch. Lightly flour a clean work surface and knead the dough until it is soft, about 8 minutes. Lightly oil a large bowl and place in the dough and cover with plastic wrap. Store in a warm place until the dough doubles in size, about 1 hour.
Lightly flour a work surface, roll out the dough to about ¼ inch thick, and using a round biscuit cutter or drinking glass, cut out 20 rounds. Place on a baking sheet lined with parchment paper, cover, and let rise for 15 minutes.
In a medium saucepan over medium heat, heat the oil to 370 degrees. Using a slotted spoon slowly add in the donuts, cooking 4 at a time, until golden brown making sure to turn at least once. Remove the donuts carefully from the oil using the slotted spoon and transfer to a paper towel lined baking sheet. While the donuts are still warm, roll in sugar, and set aside to repeat the process for the rest of the donuts.
Fill a pastry bag with a #4 tip with the strawberry preserves. Using a wooden skewer to make a hole in the side of each donut. Place the pastry tip into the hole and pipe in about 2 teaspoon of strawberry preserves. Repeat the same process with the remaining strawberry preserves donuts.