Heat ¼ cup water to 105°F* and stir in the yeast. Let sit for 5 minutes. Heat the remaining ½ cup of water to boiling and off the heat to let cool slightly.
In the bowl of a stand mixer fitted with the dough hook attachment, combine the sugar, shortening, salt, cream, egg, flour, the boiled water, and the yeast mixture.
On medium speed, knead the dough until combined and a smooth and soft dough forms. The dough should not be sticky. Cover the dough loosely with a dish towel and let rest for 30 minutes.
Place two layers of cheesecloth on the counter. Dust generously with flour. Turn the risen dough onto the cheesecloth and roll out to ¼-inch thick. Cut out Mickey Mouse shapes using a Mickey Mouse cookie cutter**. Unused scraps can be combined and re-rolled for additional cuts.
Cover loosely with a dish towel and let rest for 1 ½ hours.
During the last 10 minutes, heat 3-inches of oil over medium heat to 300°F***, as measured by an instant-read thermometer. Once the temperature has reached 300°F, use a metal spatula to gently lift the beignets and transfer into the oil. Let the beignets float to the surface and watch carefully as they begin to inflate. After a few seconds of inflating, flip the beignet over and fry until golden brown. Flip the beignet again if more time is needed to achieve a golden brown exterior on the first side.
Transfer the beignet to a paper towel-lined cooling rack. Let cool for 5 minutes, just until warm. Toss in a bowl of powdered sugar and serve immediately.
Notes
*I heated the water in a microwave-safe bowl for 20 seconds and checked the temperature with an instant-read thermometer. It’s important to not exceed 105°F so that the yeast cells do not get destroyed.**Alternatively, a sharp knife can be used to cut out squares or a biscuit cutter can be used to cut out rounds.***The temperature will continue to rise. The optimal frying temperature is 350°F. If the beignets brown too quickly, check the temperature and adjust accordingly to lower the heat.