Mix in the remaining 10 tablespoons granulated sugar, the eggs, vanilla, and buttermilk.
Stir the bread flour, shortening, and salt into the yeast mixture until a thick paste forms.
With the mixer on low speed, add the all-purpose flour 1/2 cup at a time. Mix until the dough is soft and pulls away from the sides of the bowl, 3 to 5 minutes.
On a lightly floured surface, knead for an additional minute and form it into a large ball. If the dough is too sticky, add more flour as needed.
Grease a large bowl with the oil and add the dough. Roll the dough into the oil to completely coat. Cover the bowl with a clean cloth and let rest at room temperature until doubled in size, 1 to 2 hours.
Pour 4-inches of oil into a large heavy-bottomed pot fitted with a candy thermometer. Heat the oil over medium heat to 350F.
On a lightly floured surface, roll out the dough to a ½ inch thickness. Cut out beignets with the star cookie cutter.
Line a baking sheet with paper towels. Working in batches of a few at a time, fry the beignets until golden brown, 1 to 2 minutes per side. Drain the beignets on the paper towels.