In a large bowl or stand mixer, add warm water, yeast, and 1 tablespoon sugar. Let sit for 5 minutes until bubbly.

Once bubbly, add 1/2 cup granulated sugar, shortening, egg yolks, and vanilla. Beat together until the shortening is broken up but not blended in.

Add 1 cup of bread flour, then add salt and baking powder on top of the flour. Stir into the flour slightly, then beat into the dough for about 1 minute.

Gradually add remaining flour 1 cup at a time while mixing. Knead for about 5 minutes until smooth.

Shape dough into a ball and transfer to a floured baking sheet. Form a 6×6 inch square and cover with a cloth.

Preheat oven to 350°F for 30 seconds, then turn off. Place the dough in the oven to rise for 1 hour or until doubled.

Meanwhile, bring a large pot of water to a boil. Lightly flour another baking sheet.

Once dough has risen, turn it onto a floured surface and roll into an 11×12 inch rectangle. Cut into 12 rectangles.

Transfer dough rectangles to a floured baking sheet, spacing them at least 2 inches apart. Let rise in the warm oven for 45 minutes until doubled.

Heat peanut oil to 350°F in a large pot. Cook the donuts in batches for 30-40 seconds, flipping halfway until golden brown.

Remove donuts and let them drain on paper towels. Allow donuts to cool completely.

Whisk together icing ingredients in a bowl, adjusting hot water or sugar to achieve a dipping consistency.

Dip the roundest side of donuts into the icing and let the excess drip off. Place on a wire rack to harden for 15-20 minutes before serving.