Mash potatoes – Peel and cut the potato into chunks. Steam for 10-15 minutes or until the potato is tender. Remove from the steamer and mash the potato with a potato masher or food processor. Set aside.
Mix dry ingredients – In a bowl of a stand mixer fitted with a dough hook attachment, mix together bread flour, granulated sugar, and instant yeast. Start mixing to combine them.
Add wet ingredients – Add egg yolk, milk, and mashed potatoes. Mix on low speed until dough forms. While the mixer is running, add margarine/butter and salt.
Knead – Beat until the dough is smooth and elastic. Gently lift up a piece from the surface and stretch it between two fingers to check if the dough passes the windowpane test. If properly kneaded, the dough should stretch, without tearing or breaking, into a thin membrane that you can see through.
First proof – Shape the dough into a ball and put it into a greased big bowl. Cover the bowl with a damp kitchen towel and place it in a warm spot for 30-60 minutes or until doubled in size.
Divide dough – Punch down the dough and turn the dough out onto a surface. Knead the dough a few times to push out any air bubbles. Divide the dough into 12-14 equal portions or about 40-43 gr each in weight.
Shape – Rotate the dough between your hands in a circular motion to shape them into balls. Put the balls on a lightly floured baking pan.
Rest – Cover with a kitchen towel and allow to rise for 15 minutes.
Shape into donuts – Slightly press and flatten the balls with your hand. Use a 1-inch/2.5 cm ring cutter to punch a hole in the middle.
Second proof – Cover with a kitchen towel and allow to rise for 30 minutes.
Fry – Heal oil for deep-frying to 350F/180°C in a large frying pan or skillet. When the oil is hot, drop 3-4 doughnuts at a time. Put a chopstick in the doughnut hole and spin the doughnuts as they fry to prevent the hole from closing. Allow the bottom to become golden brown before turning to the other side, about 1-2 minutes per side.
Cool – Remove the doughnuts from the oil when they are golden brown in color. Place them on a baking rack to cool completely.
Add toppings – Spread margarine/butter on top of the doughnuts. Dip the doughnuts into a bowl of chocolate sprinkles. Enjoy!