To make the pumpkin beignets: Sprinkle yeast over warm water in a small bowl, stirring to dissolve. Let stand for 5 minutes.
Combine flour, pumpkin puree, sugar, heavy cream, hot water, egg, shortening, salt, and yeast mixture in a large bowl. Mix dough just until combined and smooth. Let dough rest in bowl, covered with a clean kitchen towel, 30 minutes.
Transfer dough to a well-floured surface. Pat to about 1/4-inch thickness and cut into 2-inch squares (or use a floured Mickey Mouse-shaped cutter to cut the dough). Cover with a clean kitchen towel and let dough rise in a warm, draft-free area, about 1 to 1 1/2 hours.
Heat 2 to 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 or a slotted spoon and place on paper towels to drain.
To make the maple glaze: Combine butter and maple syrup in a medium microwave-safe bowl. Microwave until butter melts. Whisk in powdered sugar until smooth. Drizzle warm beignets with maple glaze and serve immediately.