1. Warm the milk until steaming but not boiling, then stir in the oats, butter, molasses, and brown sugar. Let the mixture rest for 10 to 15 minutes until the butter melts and the oats soften.

2. In a small bowl, stir the yeast into the warm water and let it sit for 5 to 10 minutes until foamy.

3. Add the oat mixture, yeast mixture, egg, salt, and 3 cups of flour to a large bowl. Mix until a sticky dough forms.

4. Add the remaining flour gradually, only as needed, until the dough pulls away from the bowl but still feels soft and slightly tacky.

5. Knead the dough by hand for 8 to 10 minutes or with a dough hook for 5 to 6 minutes, until smooth and elastic.

6. Place the dough in a greased bowl, cover, and let it rise in a warm place for 1 to 1 1/2 hours, or until doubled.

7. Punch down the dough gently, divide it into 15 equal pieces, and shape each piece into a smooth roll.

8. Arrange the rolls in a greased or parchment-lined 9×13-inch baking dish. Cover and let rise for 35 to 45 minutes, until puffy.

9. Preheat the oven to 375°F. Whisk the egg with 1 tablespoon milk, brush over the rolls, and sprinkle with oats.

10. Bake for 20 to 24 minutes, until the tops are golden brown and the rolls are cooked through. Cool slightly before serving.