Grease a 12-cup muffin tin and a large bowl. Set them aside.
Heat milk in a saucepan over medium heat just until bubbles begin to form. Stir in sugar, shortening, and salt; set aside until cooled to 110 degrees F (43 degrees C).
Sprinkle yeast over warm water and set aside until foamy, about 5 minutes.
Beat egg in a large bowl, then stir in yeast and milk mixtures until combined. Stir in 1/2 of the flour until no lumps remain, then stir in remaining flour, a little at a time, until a smooth dough forms. Place into the prepared bowl, turning once to grease the top of dough. Cover the bowl and let dough rise until doubled in size, about 2 hours.
Deflate dough and transfer to a well-floured work surface. Divide dough into 36 equal pieces and shape into balls. Place 3 balls into each prepared muffin cup. Cover and let rise in a warm place until dough balls double in size, about 1 hour.
Preheat the oven to 400 degrees F (200 degrees C).
Bake in the preheated oven until golden, 12 to 15 minutes. Serve warm.
