I make this bread all the time. No need for store bought. You can change the grain or the fat its very forgiving. Maybe add a cup or two of wheat instead of bread flour or instead of butter use olive oil. Add more sugar for wonderful sweet rolls.
Add Milk, boiling water, butter, oil, sugar, salt and vinager to a bowl and stir till butter melts. add most of the whipped egg saving enough to brush onto the shaped bread loaf. Set that aside and let it turn thick and curdles.
Mean time mix flour and dry yeast in a mixing bowl. add wet ingredients and mix till smooth and not sticky anymore. The more you kneed the bread dough the better. when finished oil the outside of the dough ball and let double in size.
After the ball has doubled in size turn on oven to 375 degrees. Then kneed the bread dough again and shape into a loaf. Make relief cuts if any and brush with remaining egg mixture. Then I like to sprinkle Kosher salt and Sesame seeds on it. When loaf is double in size or more, slide into oven for 20 to 25 mins, turning once at 10 minutes.