Pour the water over 1 cup oats in a medium bowl. Stir in molasses; let stand until mixture registers 115 degrees on an instant-read thermometer, about 10 minutes.
Coarsely grind 1/2 cup oats in a food processor. Transfer to a separate medium bowl; add flours and powdered milk.
Sprinkle oat-molasses mixture with yeast. Stir in 1 cup flour mixture, and then the salt. Gradually stir in remaining flour mixture, about 1 cup at a time.
Turn dough out onto a lightly floured work surface. Knead until smooth and no longer sticky, 5 to 10 minutes.
Oil a medium bowl with 1 teaspoon oil. Transfer dough to bowl; turn to coat. Loosely cover with plastic wrap, and let dough rise in a warm spot until doubled in bulk, 1 to 1 1/4 hours.
Brush a heavy-duty baking sheet with 1 teaspoon oil; set aside. Punch down dough. Transfer to a lightly floured work surface. Knead dough once or twice. Flatten into a 9-inch circle.
Pull edges of dough up and in toward center; pinch to seal. Turn dough over. Pull down on dough with cupped hands to stretch top; pinch edges at bottom. Wrap hands around sides of dough; rotate to shape into a tight ball, 5 1/2 inches in diameter and 3 3/4 inches high. Place on oiled baking sheet, seam side down.
Brush plastic wrap with remaining teaspoon oil; cover dough. Let rise until doubled in bulk, 45 minutes to 1 hour.
Preheat oven to 400 degrees. Score an X in top of dough. Brush with egg white; sprinkle with remaining tablespoon oats. Bake 10 minutes. Reduce oven temperature to 350 degrees. Bake until dark golden brown and bottom sounds hollow when tapped, 40 to 45 minutes. Let cool completely on a wire rack.