Heat milk to 130°.
Remove from heat; add shortening and sugar, stirring until shortening melts.
Cool to 100° to 110°.
Combine yeast and warm water in a 1-cup liquid measuring cup; let stand 5 minutes.
Combine milk mixture, yeast mixture, flour, and 1 teaspoon salt in a large bowl; stir well.
Turn dough out onto a heavily floured surface; knead until smooth and elastic (about 3 minutes).
Place dough in a well-greased bowl, turning to grease top.
Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in bulk.
Punch dough down, and place in a greased 13- x 9-inch pan; gently press dough evenly in the pan.
Cover and let rise in a warm place, free from drafts, 40 minutes or until doubled in bulk.
Combine egg and next 4 ingredients; spread over top of dough.
Sprinkle with caraway seeds.
Bake at 425° for 15 minutes.
Serve warm.