In the bowl of a stand mixer with a dough hook attached, mix the water, yeast and brown sugar. Let the yeast proof for 5-10 minutes. The surface should be foamy like root beer. If it’s not, then your yeast is dead and you need to start over with fresh yeast.
Add the milk, melted butter, salt and eggs to the yeast mixture. Stir briefly to combine.
Add 5 cups of the flour and the quick oats. Turn the mixer on low to start. When the majority of the flour is combined, increase to medium speed. Mix on medium speed for 5 minutes.
Stop the mixer halfway through to scrape down the dough hook, if needed. Add the remaining 1/2 cup of flour a tablespoon at a time if the dough is too wet. The dough should clean the sides of the bowl and won’t stick to your fingers when you touch it.
At the end of the mixing time, transfer the dough to a large bowl and cover with plastic wrap or a clear plate and let the dough rise in a warm place until doubled in bulk.
Grease a 9×13 pan with pan spray or butter and set aside. Punch down the dough and divide into 24 golf ball sized rolls. If you have a kitchen scale, the dinner rolls should be about 2 ounces each. Let the rolls rise until doubled in size. While the rolls are rising the second time, preheat your oven to 400℉.
Bake for 15-20 minutes or until the rolls are a deep golden brown.
Brush the rolls with 1 Tablespoon of melted butter as soon as they come out of the oven. Serve warm with butter.