In small saucepan, heat milk until bubbles form around edge of pan; remove from heat.
Stir in shortening, honey, and salt until shortening is melted.
Cool to lukewarm.
Sprinkle yeast over warm water in large bowl; stir until yeast is dissolved.
Stir in milk mixture and eggs.
Combine all-purpose and whole-wheat flours.
Add two thirds flour mixture to yeast mixture; with electric mixer at low speed, beat until blend- ed.
Then beat at medium speed until smooth— about 2 minutes.
With wooden spoon, gradually beat in remaining flour mixture.
Then beat, stretching dough 20 to 30 times.
Cover with waxed paper and a towel.
Let rise in warm place (85F), free from drafts, until double in bulk—about 1 hour.
Lightly grease a 2-1/2- or 3-quart casserole or heatproof bowl.
Punch down dough, and beat with spoon until smooth—about 30 seconds.
Turn into casserole.
Cover, and let rise until double in bulk— 20 to 30 minutes.
Preheat oven to 375F.
With a sharp knife, cut a 4-inch cross about 1/2 inch deep in top of dough.
Bake 45 to 50 minutes, or until bread is nicely browned and sounds hollow when rapped with knuckle.
Remove from casserole to wire rack.
Rub butter over top of bread.
Serve slightly warm.
Cut in wedges.
Makes 1 round loaf.