Scald the milk in a saucepan. Pour over the shortening, sugar and salt in a large mixing bowl. Cool to lukewarm. Sprinkle the yeast over the lukewarm water and stir to dissolve. Add the yeast mixture, 3 cups of the flour, and eggs to the milk mixture. Beat, using an electric mixer set on medium speed, for about 2 minutes. Gradually stir in enough of the remaining flour to make a soft dough. Turn the dough out on a lightly floured surface and knead until smooth and satiny, about 8 to 10 minutes. Place the dough in a greased bowl, turning once to grease the top and cover. Let rise in a warm place until double, about 1 hour. Punch the dough down and divide the dough into thirds, then let the dough rest for 10 minutes. Divide each third into 12 pieces and shape each piece into a ball. Place 12 balls, equally spaced, in a greased 9-inch round cake pan. Repeat for the remaining two thirds. Cover and let rise until doubled, 45 to 60 minutes. Bake in a preheated 400 degree F. oven for 12 to 15 minutes or until golden brown. Remove from the pans and cool on wire racks.