Sprinkle yeast over warm water in a small bowl, stirring to dissolve. Let stand for 5 minutes.
Combine sugar, shortening, salt, heavy cream, egg, flour and boiling water in a large bowl; stir in yeast mixture. With the dough hook attachment of an electric mixer on medium speed, mix the dough just until combined and smooth. Let dough rest for 30 minutes.
Roll to 1/4-inch thickness and cut individual beignets into 2 1/2 to 3-inch squares. Cover with a towel and let dough rise until doubled in size in a warm, draft-free area, about 1 to 1 1/2 hours.
Using caution, heat 3 inches of vegetable oil to 350°F in a deep, heavy pot over medium-high heat. Fry beignets until golden brown, about 2 to 3 minutes, turning as soon as they brown on one side. Remove with tongs and place on paper towels to drain. Dust warm beignets with powdered sugar and serve immediately.