Combine milk, shortening, sugar, and salt in a saucepan and cook, stirring, over medium heat until sugar dissolves. Remove from heat; set aside to cool.
Dissolve yeast in 1⁄4 cup lukewarm water in a large bowl; set aside until foamy, about 10 minutes.
Pour milk mixture into yeast. Stir in eggs and gradually add flour. Stir with a wooden spoon until dough gets stiff, then use your hands (dough will be sticky, so grease your hands with a little butter). Brush a small amount of butter on the inside of a large bowl and on one side of a sheet of waxed paper. Place dough in bowl, cover with buttered wax paper, and lay a damp dishcloth on top. Set aside to rise until doubled in bulk, at least 3 hours.
Turn out dough onto a lightly floured surface. Knead until elastic, then roll out to 1⁄2" thickness. Cut dough with a 3" biscuit cutter, dip each round into melted butter, and fold in half. Line up, round edges up, sides touching, on a cookie sheet. Cover as in step 3, and set aside to rise, at least 2 1⁄2 hours.
Preheat oven to 350°. Bake until golden, about 15 minutes. Serve warm.