Place 1/2 cup of the water and the shortening in a small saucepan over high heat. Heat over high heat until the shortening melts. Remove from the heat.
In the bowl to the electric mixer, add the sugar and salt. Add the hot shortening water and mix with the paddle until the sugar dissolves. Add the remaining 1/2 cup cold water to cool the mixture. Add the egg, mixing constantly. Add the yeast and mix again. Change to the dough hook and add the flour. Mix well and knead on low speed until the mixture is moist and stiff, 5 minutes. Add additional flour if needed.
Cover with plastic and place in the refrigerator overnight.
The next day, remove the bowl from the refrigerator and let sit at room temperature for 1 hour. Remove the dough from the bowl and using a pastry scraper, cut the dough into 24 equal pieces about 115 grams each.
Butter two round 9-inch cake pans. Roll each piece of dough into a round circle. Place 9 of the balls around the outside of one of the pans, making sure they don't touch each other or the edge of the pan. Place 3 of the balls in the center making sure they don't touch. Repeat with the remaining 12 balls of dough and the second pan.
Cover with plastic wrap and a towel and let rise in a warm place until double in volume, about 1 hour.
Preheat an oven to 350 F. Bake the rolls in the middle of the oven until golden on top and well puffed, 20 to 25 minutes.
Remove from the oven and let cool or serve piping hot from the oven.
1 cup water
6 tablespoons vegetable shortening
3 tablespoons sugar
1 1/2 teaspoons salt
1 egg, whisked
3 teaspoons dry yeast
3 cups all purpose flour