In a large bowl whisk together the flour, baking powder, salt, and sugar.
Stir in melted butter, warm milk, and beaten egg until a soft dough forms; do not overmix.
Turn the dough onto a lightly floured surface and knead briefly until smooth; let rest 10 minutes.
Divide the dough into 8–12 equal pieces and roll each piece into a thin round about 1/8 inch thick.
Heat 1–2 inches of vegetable oil in a deep frying pan to 350°F (175°C). Fry buñuelos a few at a time until puffed and golden, about 1–2 minutes per side.
Use a slotted spoon to transfer fried buñuelos to paper towels to drain.
Make the chocolate sauce by heating the heavy cream in a small saucepan until simmering, then remove from heat and stir in chocolate chips, butter, and vanilla until smooth.
Serve the warm buñuelos with the chocolate sauce for dipping and dust with powdered sugar if desired.