Combine the yeast, ¼ cup warm water, and sugar in a small bowl. Stir to combine and set aside for about 5 minutes.
Add the milk, butter, and brown sugar in a medium saucepan. Gently warm over medium-low heat until the mixture reaches a temperature between 100-110º Fahrenheit.
Add 2 cups of flour, salt, and ½ cup of oats to a large mixing bowl or the bowl of your stand mixer. Use the dough hook attachment (if using a stand mixer) or a whisk and stir to combine.
Add both the yeast and the milk-butter mixture to the flour mixture. Stir until all of the ingredients are well combined.
Slowly add the last 1 ½ cups of flour to the dough, ¼ cup at a time. Mixing between each add.
Once the dough comes together and is slightly sticky, turn it out onto a lightly floured surface. Knead the dough 10 times.
Grease a large casserole dish (9x13) with baking spray. Set aside.
Place the dough in a lightly greased bowl and allow it to rise for 1 ½ hours or until it doubles in size.
Transfer the dough onto a lightly floured surface and divide it into four equal quarters. Separate each quarter into thirds and roll into balls.
Roll each dough ball in the oats and place them in the prepared casserole dish. Cover with plastic wrap or a towel and allow the rolls to rise for 30 minutes.
10 minutes before the final rise time is over, preheat the oven to 375º Fahrenheit.
Brush the beaten egg over the top of the rolls before baking. This step is optional.
Bake the rolls for 25 minutes or until nicely golden brown. Remove the rolls from the oven and place them on a cooling rack.