Combine butter and honey until fully combined. Refrigerate or set aside until ready to be used.
Combine 2 tablespoons lukewarm water and yeast in a large bowl or stand mixer and let it sit until it dissolves for about 5 minutes.
Meanwhile, in a microwave-safe medium bowl, combine milk, with the butter pieces, salt. Microwave for about a minute and stir until everything is melted.
Lightly whisk in the egg and the honey to the butter mixture (if the mixture is too hot let it cool to warm to prevent eggs from curdling.)
Dump everything into the yeast mixture.
If using a stand mixer, mix on medium-high speed using a dough hook until all the ingredients are combined, or just mix by hand.
Then add 2 cups of whole wheat flour and 1 ¾ cups all-purpose flour. Continue mixing the dough and stop when the dough doesn’t stick to the sides or bottom of the bowl. Add additional flour (if needed) to make a soft dough. (It is better to have sticky dough than hard dough).
Turn the dough on a lightly floured surface and knead for 8 to 10 minutes or more if you want an airy bread. Or you may continue kneading with a dough hook for about 8 minutes.
Place the bread dough in a large greased bowl. Cover it loosely with clean clothe and let it rise in a warm, draft-free place for about 45 minutes to 1 hour or until doubled. Punch the dough down.
At this point, the dough maybe shaped into a grease loaf pan, and place seam side down in the pan or divide dough into 12 equal pieces. Shape them into balls. Place in a greased 12-inch round pans.
Brush with the honey butter mixture and bake.
Preheat the oven to 350 F. Bake for 20 to 25 minutes or until the crust is deep golden brown and the bottom of the loaf sounds hollow when tapped.
Remove from the baking pan and let it cool. Serve them warm.