Place warm water in a small bowl. Sprinkle yeast on top and stir to dissolve. Allow yeast to activate (about 5 minutes).
In a large mixing bowl or stand mixer, combine egg, cream, shortening, granulated sugar, salt, and nutmeg. Mix to combine.
Pour in activated yeast and mix.
Add flour to the mix. Use the dough hook attachment on a stand mixer and mix on medium speed until all ingredients are combined and the 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.
Heat 3 inches of oil in a deep-sided, heavy pot over medium-high heat until oil reaches between 360 and 370°F.
On a lightly floured surface, roll out the dough until it is ½ inch thick, making sure not to overwork the dough. Cut into 2½-inch squares.
Working in batches, fry beignets in the hot oil until golden brown (1–2 minutes on each side).
Use tongs to remove the beignets from the hot oil. Place on a paper towel–lined plate to drain.
While beignets are still warm, dust them completely with powdered sugar. Serve immediately.