Egg wash: 1 egg plus 1 teaspoon water(whisk together)
In stand mixer bowl, add 1 cup bread flour, yeast, salt and rolled oats; mix well. Add warm water, oil and molasses to flour mixture. Using a paddle attachment, blend on low speed for 30 seconds. Beat on medium speed for 4 minutes.
Switch to dough hook attachment. Gradually stir in walnuts, whole wheat flour, and enough remaining bread flour to make a firm dough. Knead until smooth and elastic, about 5 to 7 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.)
Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
Turn dough onto lightly floured surface; punch down to remove air bubbles. Shape into a round loaf. Place on greased cookie sheet. Cover; let rise until indentation remains after touching.
Preheat oven to 375°F.
Brush egg wash onto top of risen loaf. Sprinkle with oatmeal, if desired. Bake for 30 to 40 minutes. Remove from cookie sheet; cool on wire rack.