In a mixing bowl, combine the warm water and active dry yeast. Allow it to sit for about 5-10 minutes until frothy.
In a separate bowl, whisk together the all-purpose flour and yellow cake mix.
Once the yeast mixture is frothy, add in the melted butter and beaten egg. Mix until well combined.
Gradually add the flour and cake mix mixture to the yeast mixture. Stir until a soft dough forms.
On a floured surface, knead the dough for about 5 minutes until it’s smooth and elastic.
Place the kneaded dough in a lightly greased bowl, cover it with a kitchen towel, and let it rise in a warm place for about 1 hour.
After the dough has risen, punch it down, divide into 12 equal pieces, and shape each into a ball.
Cover the rolls and let them rise for another 30 minutes, or until they have puffed up.
Preheat your oven to 350°F (175°C).
In a small bowl, combine the beaten egg with 1 tablespoon of water. Brush the egg wash over the tops of the rolls.
Bake the rolls in the preheated oven for 15-20 minutes, or until golden brown.
Once baked, remove the rolls from the oven and allow them to cool on a wire rack.