Stir the yeast, 1 tablespoon of sugar, and the warm water together in a small bowl. Leave it alone for about 10 minutes. It should turn foamy, which tells you the yeast is alive and ready to work.
Add the flour, warm milk, egg, yolk, salt, yeast mixture, and the remaining 3 tablespoons of sugar to your mixer. Mix until a dough forms, then add the soft butter. Keep mixing until it turns smooth and very soft.
Move the dough to a lightly greased bowl and cover it well. Refrigerate it for 6 to 8 hours, or overnight. This slow rest builds flavor and makes the soft dough easy to roll out.
Dust your counter with flour and roll the dough to about ½ inch thick. Cut rounds with a 2½-inch cutter or a glass. Gather the scraps and re-roll them until you use all the dough.
Place the rounds on a flour-dusted baking sheet and cover them. Let them rise for about 20 minutes, until they look nearly doubled. In a cool kitchen, this can take longer, so be patient.
Spoon the chocolate spread into a piping bag fitted with a large round tip. Keep the spread at room temperature so it flows smoothly. This is my favorite simple chocolate donut filling recipe because it takes no cooking at all.
Heat the oil to 365–375°F and hold it there. Fry 3 or 4 donuts at a time for about 1 minute per side. Flip once and cook until they turn a rich golden brown.
Lift the donuts out with a slotted spoon or forks. Set them on paper towels to drain for a minute. Let the oil return to temperature before you add the next batch.
Poke a hole into the side of each donut with a dowel or chopstick. Wiggle it gently to make a small pocket inside. Pipe in the chocolate until the donut feels pleasantly heavy.
Roll or dust the donuts with sugar while they are still warm. The sugar sticks best at this stage. Serve right away for the softest, gooiest bite.