Scald milk by heating in a small saucepan over medium heat until bubbles appear around inside edge of pan and milk is about to boil. Pour scalded milk into a large mixing bowl. Add shortening, sugar, and salt, stir until sugar dissolves, then set aside to cool until lukewarm, about 2 minutes. Meanwhile, dissolve yeast in 1⁄4 cup warm water in a small bowl and set aside until foamy, about 10 minutes.
Add eggs and yeast mixture to milk mixture in bowl and stir with a wooden spoon until well combined. Gradually add flour, stirring until dough comes together. Turn dough out onto a floured surface and knead until smooth, about 10 minutes. Shape dough into a ball and lightly dust with flour. Transfer dough to a large clean bowl, cover with a clean, damp kitchen towel or plastic wrap, and set in a warm spot to let rise until doubled in bulk, about 1 hour.
Lightly grease two baking sheets with some of the butter and set aside. Turn dough out onto a clean surface, divide in half, then shape each piece of dough into a ball. Roll dough balls out into 14" circles, then brush each with melted butter, and cut each circle into sixteenths, making 32 wedges in all. Starting with rounded edge and working toward pointed end, roll up each wedge. Arrange rolled dough wedges, pointed-end side facing down to keep wedge from unrolling, on prepared baking sheets about 2" apart. Brush tops and sides with some of the remaining butter, loosely cover with a clean, damp kitchen towel or plastic wrap, and set aside in a warm spot to let rise for 45 minutes.
Preheat oven to 350°. Bake rolls until golden brown and hollow sounding when tapped, about 25 minutes. Set rolls aside to cool for at least 15 minutes. Serve warm or at room temperature.