Heat the milk in a saucepan over medium heat until bubbles begin to form, but the milk is not simmering. Stir in the sugar, shortening, and salt; set aside until cooled to 110 degrees F (43 degrees C). Sprinkle the yeast over the warm water and set aside for 5 minutes.
Beat the egg in a mixing bowl, then stir in the yeast and milk. Stir in half of the flour until no lumps remain, then stir in the remaining flour a little at a time until a smooth dough forms. Place into a greased bowl, turn once to grease the top, cover, and let rise until doubled in bulk, about 2 hours.
Grease a 12 sectioned muffin tin. Deflate the dough, and place onto a well-floured work surface. Divide the dough into 36 pieces, and form into balls. Place 3 balls into each muffin cup. Cover, and let rise in a warm place until doubled in bulk, about 1 hour.
Preheat an oven to 400 degrees F (200 degrees C).
Bake in the preheated oven until golden, 12 to 15 minutes. Serve warm.
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