In a large bowl, combine lukewarm water and yeast. Let sit for 5 minutes to let yeast dissolve. In a small bowl, whisk together heavy cream, sugar, salt, egg, and vanilla. Add to yeast mixture.
Mix in 2 cups of flour to wet ingredients. Add melted butter, mixing until smooth. Add additional flour as needed to make a soft, shaggy dough. It should be slightly sticky.
On a floured surface, knead for 1-2 minutes until a smooth ball forms. Place in a greased bowl, turning once to coat dough. Cover with a clean cloth and let rise in a warm space until doubled in size, about 2 hours.
Punch down dough. Place on a floured surface and roll into a large rectangle, about ¼ inch thick. Cut into 2-inch squares, and rest for 10 minutes before frying.
Heat frying oil to 375°F. Working in small batches so as not to crowd the oil, fry the dough squares until puffy and golden brown on both sides. Transfer beignets onto paper towel to drain oil. Dust with powdered sugar and serve warm. Enjoy!