Add lukewarm water and honey to a large bowl or the bowl of a stand mixer. Sprinkle with yeast, stir and let stand 5 minutes. (Mixture should be bubbling a bit after 5 minutes)
Add the whole wheat flour and the salt and mix lightly. Mix in vegetable oil. Work in all-purpose flour gradually, adding just a 1/2 cup at a time and mixing until dough comes together into a smooth, moist but not sticky dough. (I only needed to add just over 4 cups to reach this proper dough consistency).
If using a stand mixer, knead on low for about 5 minutes. If kneading by hand, turn dough out onto a lightly floured surface and knead for about 10 minutes. Add in only enough additional flour to stop the dough from sticking.
When dough is smooth and elastic, place it in a well oiled bowl. Turn it several times in the bowl to coat the surface of the dough, and cover with a plastic wrap. Let rise in a warm place until doubled, about 45 minutes.
Remove the dough from the bowl to a lightly floured surface. Divide the dough into two equal sized pieces. For each piece, press dough down while moving it into a rectangle shape, with the short side roughly as long as your loaf pan. (I used 81/2 x 41/2 inch loaf pans because I like a taller loaf but 9×5 would work as well). Roll up the dough from the short side, pinching it together with each roll. Pinch together the seam when finished and place seam side down into greased loaf pans. Allow to rise until dough doubles and crests about an inch above the edge of the baking pan in the middle (it will rise more in the oven). If desired, just before baking, spritz top of loaves with water and sprinkle with wheat bran.
Bake at 375° F for 30 – 40 minutes or until thermometer inserted in the bottom of the bread reads 195-200° F. Immediately remove bread from pans and cool completely on a cooling rack before slicing.