01 - Dissolve yeast in warm water with a pinch of sugar in a large bowl. Let stand until foamy, about 5 minutes.
02 - Add remaining sugar, milk, egg, melted butter, and vanilla to yeast mixture. Whisk until thoroughly combined.
03 - Stir in flour and salt. Mix until a sticky, shaggy dough forms.
04 - Turn dough onto floured surface. Knead until smooth and elastic, approximately 5 minutes.
05 - Place dough in greased bowl, cover with plastic wrap. Let rise in warm place until doubled, about 1 hour.
06 - Punch down dough, turn onto floured surface. Roll to 1/2-inch thickness. Cut into 2-inch squares. Cover and rest 10 minutes.
07 - Heat 2 inches vegetable oil in deep pot to 350°F.
08 - Fry beignets in batches 1–2 minutes per side until puffed and golden brown. Remove with slotted spoon, drain on paper towels.
09 - Generously dust warm beignets with powdered sugar.
10 - Heat cream in small saucepan over medium heat until just simmering. Remove from heat. Add chocolate, butter, vanilla, and salt. Let stand 2 minutes.
11 - Whisk chocolate mixture until smooth and glossy. Serve warm alongside beignets.