In a large mixing bowl or the bowl of a standing mixer, add oats and butter. 

Heat milk in a saucepan to a simmer, then pour onto the oats and butter. Mix with a paddle or spoon to combine and set aside for 1 and 1/2 hours. Mixture should be room temperature. 

Add honey, warm water, yeast, and salt and stir well to combine. 

Add whole wheat flour and mix on medium-low speed until combined. 

Add all-purpose flour a little at a time until the mixture starts to pull away from the sides of the bowl and forms a dough. Add only enough flour so the dough is soft and is not sticky. 

Mix dough for a few minutes until it is smooth and elastic. 

Transfer dough to a greased bowl and cover with plastic wrap. Allow to rise about 1 hour or until it doubles in size. 

PUnch the dough down and divide into 2 equal pieces. Shape into loaves and place into 2 lightly greased loaf pans. 

Combine egg white and water in a small bowl to create an egg wash. Brush egg wash over the top of both loaves. 

Place a well greased piece of plastic wrap gently on top of the loaves and set in a warm spot to rise until 1 inch above the pan, about 45 minutes to 1 hour. Peel off plastic wrap.

Bake at 350°F for 30-40 minutes. Loaves are done when you tap the top and it makes a hollow sound. 

Cool for 15 minutes on a wire rack before removing from the pans and cooling completely.