Bring 2 cups water to a boil in a medium saucepan; stir in oats and butter. Boil, stirring constantly, 1 minute. Remove from heat; let cool to 110°.
Stir together yeast, 1/2 cup warm water, and 1 tablespoon sugar in a 2-cup measuring cup; let stand 5 minutes.
Beat oat mixture, yeast mixture, flour, salt, and brown sugar at medium speed with an electric mixer until smooth.
Turn dough out onto a lightly floured surface; knead until smooth and elastic (about 5 minutes). Place in a well-greased bowl, turning to grease top.
Cover and let rise in a warm place (85°), free from drafts, 1 hour or until dough is doubled in bulk.
Punch dough down, and divide in half; shape each portion into 16 (1 1/2-inch) balls. Place evenly into 2 lightly greased 9- x 1 3/4-inch round cakepans.
Cover and let rise in a warm place (85°), free from drafts, 30 minutes or until doubled in bulk.
Bake at 375° for 15 minutes or until golden brown.
Note: Reserve 1 portion of dough for Cinnamon Rolls recipe, if desired.