Place oats in a food processor, and process until a fine flour forms.
Add bread flour, and process until combined.
Make the tang zhong. Take 1/3 of a cup of your oat flour + bread flour mixture, add to a small pan, and add 1 cup of milk. Stir to combine, and place the mixture over medium heat. Stir with a wooden spoon continually until a thick, pudding-like mixture forms, about 3 to 5 minutes. Take off the heat immediately.
In a stand mixer, place the tang zhong, the rest of the flour mixture, the rest of the milk, the butter, the yeast, the salt, the honey, and the eggs. Knead until the dough is extremely silky and smooth, about 10 to 15 minutes. If you do not have a stand mixer, you can use a food processor, but most food processors do not have room for so many ingredients, so you will have to divide the mixing into three batches and bring them together by hand at the end.
Place the dough in a bowl (or keep it in the bowl of your stand mixer), and cover. Let it rise in a warm place until doubled in size, which will take about 1 hour.
(optional) Once doubled, place dough in refrigerator at least overnight and up to three days; this resting period helps develop gluten and flavor.
Punch down dough and divide into eight roughly equal pieces.
Roll each piece into a ball. Line four of the balls into one loaf pan; repeat with the four others in another loaf pan.
Allow the loaves to double in size, about 1 hour. Meanwhile, preheat the oven to 350°F.
Right before placing the loaves into the oven, apply an egg wash: Beat an egg, then brush on top of each loaf.
When done proofing, place the loaves into the oven and bake for 35-40 minutes, or until the loaves hit an internal temperature of 205-210°F.
Pop the loaves out of the pans, and allow to cool completely.