Place warm water in a small bowl. Sprinkle yeast and 1 Tbsp sugar over water. Stir to combine. Let sit for 5-7 minutes until yeast mixture is foamy on top.
In a large bowl, whisk together remaining sugar, flour, baking powder, and salt. Set aside.
In the bowl of stand mixer fitted with a paddle attachment, combine egg yolks, shortening, and vanilla extract. Mix until yolks and shortening has been broken up.
Add yeast mixture and switch out paddle attachment with dough hook attachment. Add flour mixture in three additions. Mix on low-medium speed until all the flour has been incorporated. Then increase speed and mix/knead for 2 minutes or so until the dough is smooth.
Remove dough from mixing bowl and place onto a light floured baking sheet. Pat dough into a rectangle with a thickness of about ½ inch. Cover with a kitchen towel and set up a proofing box in your oven.
In a medium sauce pot, bring about 4 cups of water to a boil. Place sauce pot in the bottom rack of oven. Place the towel covered dough in the oven. Close the oven door and let the dough rise for about 45 minutes to 1 hour, until the dough has almost doubled in size. Do not open the oven door during the time, keep in as much heat and steam in the oven as possible.
Remove dough from proof box oven and place on a lightly floured work surface. Pat dough into a rectangle about 18x13-inches. Use a sharp knife (or pizza cutter) to cut the bars into 3-inch squares.
Gently transfer squares to lightly floured baking sheet. You will need two baking sheets. Arrange squares at least 1 ½ inches apart from each other. Bring water in sauce pot to a boil once more and place in the bottom rack of oven. Keep squares uncovered and place in the oven for another 30-45 minutes until they have doubled in size.
Fill a large pot with 3 inches of oil.* Using a candy thermometer to measure the temperature, heat oil to 350°F.
Remove dough squares from the oven. Brush off any excess flour and carefully place 2-3 squares into the hot oil. Be sure not to crowd the doughnuts. Set a timer and fry for 35 seconds, until light golden brown in color. Carefully turn over the bar and fry the other side for another 30 seconds. Once golden brown all over, remove cooked doughnut from oil and let drain over a cooling rack set over paper towels. Allow squares to cool before dipping in sugar glaze.