Add 3/4 cup warm water to a small bowl. Sprinkle 1 tsp yeast on top and stir to dissolve. Allow the yeast to activate (about 5 minutes).
In a large mixing bowl (or stand mixer), add the sugar, egg, salt, nutmeg, heavy cream and shortening. Mix to combine.
Pour in the activated yeast and mix.
Add the flour to the mix. Use the dough hook attachment on a stand mixer and mix on medium speed until all of the ingredients are combined and dough is smooth but still slightly sticky.
Form a ball with the dough and place in a greased bowl. Cover and let rise for about 1 hour.
Use a deep sided heavy pot and add 3 inches of vegetable oil. Heat over medium high heat until oil reaches between 360°F - 370°F (cooler than this won't cook the beignets fast enough and hotter than this will burn them quite easily).
On a lightly floured surface roll out the dough until it is 1/2 inch thick. Cut into 2 1/2 inch squares.
Working in batches fry the beignets until golden brown, about 1 minute on each side.
Use tongs to remove the beignets from the hot oil. Place on a paper towel lined plate to drain. While the beignets are still warm, dust them completely with powdered sugar. Serve immediately.