In a medium bowl, whisk together yeast, sugar, 1 cup all-purpose flour and milk. Cover with plastic wrap or a towel and let rise until doubled, about 1 hour.
Pour 1/2 cup old-fashioned oats into a food processor; pulse until fine-ground. Pour ground oats into a large bowl and add remaining cups of flour and salt; stir to combine. Add yeast mixture, egg yolks and oil. Add water and stir to combine (add more water as needed until dough forms, up to 1/2 cup total).
Knead dough with dough hook in stand mixer on medium speed for 3 minutes (or by hand on a lightly floured surface for 5 minutes) or until dough is smooth and elastic. Shape dough into a ball; place in a well-oiled bowl. Cover with plastic wrap or a towel and let rise until doubled, about 1 hour.
Preheat oven to 400 degrees F. Lightly grease two 9-inch round cake pans and set aside.
Punch down dough and divide into 24 equal pieces. Roll each piece into a ball. Place 12 balls in each cake pan about 1/2-inch apart. Cover with plastic wrap or a towel and let rest 25-30 minutes.
Brush rolls lightly with egg white, then sprinkle with more old-fashioned oats (about 2 tablespoons). Bake until golden brown, about 25-30 minutes. Place pans on a cooling rack to cool slightly; serve warm.
Disclosure: I received compensation from Gold Medal Flour for recipe development purposes. All opinions are my own.