In the bowl of your stand mixer with dough hook attached, combine flours, brown sugar, salt, yeast, milk, and water. Mix on low until a rough dough comes together.
Add half of softened butter and continue to mix until completely incorporated into the dough. Add the remaining butter and repeat.
Continue to mix dough on low/low-medium until you have a smooth stretchy dough that does not stick to the sides of the bowl.
Remove dough, shape into a ball. Lightly grease your mixer bowl and place the dough in then cover. Leave in a warm place to proof for 1-2 hours. Dough is ready when it has doubled in size.
Prepare an 8.5x4.5 loaf pan with parchment paper. Set aside.
Punch down the dough and pat out into a rectangle that is about 8x10". Roll up into a log and place into your loaf pan seam side down.
Cover your loaf pan and allow the dough to proof again for about 45 minutes. Preheat your oven to 350°F while your dough proofs. Dough will be domed and the dome will be just clearing the edge of the pan.
When dough is ready, brush the top with egg white then sprinkle your oats.
Place your dough on the center rack of your oven, baking for 40 minutes.
Remove pan from oven and transfer your dough to a wire cooling rack. Let dough completely cool before slicing into. Store in an airtight container. Enjoy!