In the bowl of your mixer, place all dry ingredients (flours, salt, gum, etc) , except for those used in step 2 and blend on low for about 1 minute to fully integrate all ingredients (or you could sift it, but this is the lazy way).
While you're sifting, mix yeast and sugar into the lukewarm water in a mug or bowl. If after 5-10 minutes your mixture is not foaming, your yeast is dead. Start again. You should smell yeast and have something that looks like beer head on the top of your water. You absolutely cannot make this bread rise without yeast, so this is not a step to skip.
Add the butter and vinegar to the mixer, fully integrating before you begin to add your eggs. I usually add the whole egg and while it's mixing, separate the whites into a separate bowl and then dump all three in at once. Last, but not least, add the yeast slurry (but only if it's properly proofed! See step 2).
Mix on medium-low until everything is integrated. I like to beat for an additional minute or two on high to be sure that everything's nice and slapped around. This is also where I add any herbs or seasonings I want to integrate into the batter (frequently 1 tbsp of garlic granules, 2 teaspoons rosemary and 1 tbsp black pepper, but use what you like).
Now, this is where you have a decision to make. This recipe makes great rolls, ok buns and wonderful bread.
For rolls: Find two muffin pans. Fill the cups about half way until you run out of batter. You won't probably get two dozen, but you'll get something like 18 or so.
For buns: Using a Texas muffin pan, fill each slot equally.
For bread: Scoop all the dough into a regular loaf pan. The loaf usually draws up a little for me during baking, making it really easy to get out.
Whatever you choose, allow the dough to rise at least an hour. I've left for the grocery and come back as many as 3 hours later and still had a really great rise. Cover loosely with cellophane to keep bugs and things out. :) After you've given it proper rise time, sprinkle with a topping (if you like) and insert into a 400°F oven.
Bake rolls for about 25 minutes and then check for doneness, buns for about 30 and check and bread for 45 minutes. If the bread has a hollow sound when you thump it, it's done. It will be really crusty (and that's the way we like it).