Add milk, sugar, yeast and oats to a large mixing bowl. Stir and let rest for 10 minutes until bubbly.
Add 2 cups flour, butter, salt, eggs. Mix.
Continue adding flour, 1 cup at a time. You might not need to add all the flour.
Knead dough for 5 minutes by stand mixer, or 10 minutes by hand.
Place in a lightly sprayed bowl, cover and let rise until doubled.
Lightly punch down and divide dough into quarters. Take each quarter and divide into 24 equal sized pieces. Shape each piece by cupping your hand over the dough and rotating in a circular motion. Place rolls on a lightly sprayed baking sheet. If you want soft sides, place rolls next together. If you want a round roll browned all over, space your rolls apart.
Cover and let rise, about 30-45 minutes.
Just before baking, brush tops lightly with melted butter.
Bake at 400 degrees for 15-18 minutes.
Brush with melted butter when they come out of the oven.
Transfer rolls to a cooling rack.