In the bowl of a stand mixer, combine the warm water, sugar, and yeast. Mix well, then let sit for 5-10 minutes, or until the yeast is frothy and bubbly.
Add the oil, honey, salt, and half of the wheat flour into the yeast mixture and mix on low using the dough hook until combined - about 1-2 minutes.
Continue adding one cup of flour at a time, then mixing on low speed, until the dough pulls away from the sides and looks smooth. Once you have added in all of the flour that you need, knead the dough on medium speed for about 3 minutes. The dough should be smooth and elastic.
Cover the bowl with plastic wrap and let rise in a warm place until doubled in size, about 45-60 minutes.
Grease three 8.5" x 4.5" bread pans with butter.
Once your dough has doubled, divide into 3 even pieces. Sprinkle flour on your counter, then very gently roll each portion into a roughly 8"x12" rectangle using a rolling pin (the shorter side of the rectangle should be about the length of your baking pans).
Starting at the shorter end, roll each rectangle up tightly, then pinch the end to seal the seam. To shape dough, tuck each of the ends under and place seam-side down into one of your prepared loaf pans. Repeat with the other two portions.
In a small bowl, add the egg and water and whisk. Brush a thin, even layer over the tops of each loaf of dough using a pastry brush, then let rise again until doubled in size, about 30-45 minutes.
Preheat your oven to 350 degrees F. Once your loaves have doubled in size, bake all three at the same time for 28-30 minutes, or until golden brown (an instant-read thermometer should read 190-195 degrees F when inserted into the center of your loaves).
Remove from the oven and brush melted butter over the top of each loaf of bread. Let cool for about 10-15 minutes, then remove from the baking pans and let cool completely on a wire rack before slicing. Enjoy!