Soften Oats in Warm Milk: Place the oats and softened butter into the bowl of a stand mixer or a large mixing bowl. In a saucepan, bring the milk just to a simmer, then carefully pour it over the oats and butter. Stir gently to combine. Let the mixture sit uncovered for about 90 minutes to cool and allow the oats to absorb moisture. The mixture should reach room temperature before proceeding.
Activate Yeast and Combine Ingredients: Stir the honey, warm water, instant yeast, and salt into the oat mixture. Mix until evenly blended. Add the whole wheat flour and begin mixing on medium-low speed (or by hand) until a shaggy dough forms.
Form the Dough: Gradually add the all-purpose flour, starting with 2¼ cups. Add more only as needed until the dough begins pulling away cleanly from the sides of the bowl. The dough should be soft and slightly tacky but not overly sticky. Knead with a dough hook or by hand for about 5–7 minutes, or until the dough is smooth and elastic.
Let the Dough Rise (First Proof): Lightly oil a large clean bowl and place the dough inside, turning once to coat. Cover with a clean kitchen towel or plastic wrap and let it rise in a warm environment until it doubles in size, about 1 hour.
Shape and Prepare for Second Rise: Punch down the risen dough and divide it into two even portions. Shape each portion into a loaf and place into two lightly greased 9x5-inch loaf pans. Brush the tops with egg wash, then sprinkle additional oats over each loaf if desired.
Second Rise: Cover the loaf pans loosely with greased plastic wrap and let the dough rise again in a warm spot until the loaves have risen about 1 inch above the rim of the pans—this should take 45 to 60 minutes. Gently remove the plastic wrap once fully risen.
Bake to Perfection: Preheat your oven to 350°F (175°C). Bake the loaves for 30–40 minutes, or until they sound hollow when tapped on top, or a thermometer inserted into the center reads 200°F (93°C). Remove from oven and let cool in pans for 15 minutes, then carefully turn out onto a wire rack to cool completely.