In a small saucepan over low heat warm the water, milk, butter and honey until butter is melted and mixture is smooth. Cool for a few minutes, or until 120-130°F.
In the bowl of a stand mixer fitted with a dough hook, or in a large bowl if you plan to mix by hand, combine 2 cups of the whole wheat flour, oats, yeast and salt. Add the milk mixture and mix until combined. Add the remaining whole wheat flour 2 tablespoons at a time until the dough is still sticky but clears the side of the bowl. You may not need all 3 ½ cups flour, or it's possible you'll need a bit more.
Continue to mix or knead by hand until smooth and elastic (7-8 minutes with a mixer, 15 minutes by hand). Place dough in a grease bowl, cover and let rise in a warm place until doubled, about 1 hour.
Gently punch down dough and knead a few times. Roll dough out on a lightly floured surface into a rectangle 9 inches wide. Starting with a short end, roll up the dough. Place seem side-down in a greased 9x5-inch loaf pan. Cover with plastic and let rise until doubled again, about 1 hour.
Preheat oven to 400°F. Brush top of loaf with egg wash and sprinkle with oats, if desired. Bake until crust is dark golden brown and loaf sounds hollow when tapped, about 45-50 minutes. Remove from pan and let cool for at least 20 minutes before slicing.
Calories: 322kcal, Carbohydrates: 58g, Protein: 11g, Fat: 7g, Saturated Fat: 3g, Cholesterol: 26mg, Sodium: 212mg, Potassium: 302mg, Fiber: 8g, Sugar: 7g, Vitamin A: 177IU, Calcium: 52mg, Iron: 3mg