To activate the yeast, combine the warm water, molasses, and yeast to the bowl of your stand mixer. Cover with a clean kitchen towel and let it sit for 5 minutes. The yeast should be bubbling at this point.
To the yeast mixture, add the whole wheat flour, egg, olive oil, apple cider vinegar, and salt. Once everything is mixed together, cover the bowl with a clean kitchen towel, and let it sit for 30 minutes.
Add the rest of the all-purpose flour and the tangzhong roux to the mixing bowl, and combine lightly. Attach your dough hook to the mixer and turn it on to a medium speed. Knead the dough for 7 minutes. It should start to pull away from the sides of the bowl and be soft but not sticky.
Grease a large bowl with baking spray or olive oil and then transfer the dough to the bowl. Cover the bowl with plastic wrap or a clean kitchen towel. Let it proof in a warm place for 45 minutes.
Uncover the dough and punch it down a bit. Cover again and let it proof for 45 minutes, or until it is fully doubled in size.
Preheat oven to 350 degrees F.
Grease an 8x4 loaf pan with baking spray. Take the doubled dough out of the bowl and shape it into a loaf. Place it in the tin and cover it with plastic wrap. Proof it for 30 more minutes, or until an inch above the sides.
Bake the loaf in the preheated oven for 30 minutes, or until it's golden brown and it sounds hollow when you tap the top. Let the bread sit for 10 minutes before you remove it from the pan.
Remove bread from the pan and finish cooling it on a wire rack or large plate.