In a large bowl of an electric stand mixer, dissolve yeast in 1½ cups warm water. Let stand until creamy, about 10 minutes.
Stir in flour and cake mix. Mix until the dough is smooth.
Lightly oil a large bowl, place the dough in the bowl and turn to coat with oil. Cover with a damp cloth and let rise in a warm place until doubled in volume, about 1 hour.
Deflate the dough and turn it out onto a lightly floured surface. Divide the dough into two equal pieces and form into rounds. Let rest for 5 minutes.
Roll each piece into 12-inch circles.
Cut each circle into 10 wedges. Brush melted butter onto the circles.
Roll up the wedges, beginning at the wide end. Place the rolls on parchment-lined baking sheets.
Whisk together egg and 1 Tbsp water. Brush the rolls with the egg wash. Cover and let rise until doubled, about 25 minutes.
Preheat the oven to 350ºF.
Bake the rolls for 15 to 18 minutes, or until golden brown.
