Sometimes my best (or wackiest) ideas come to me in the middle of the night. This was one of them. Be sure to use the ripest bananas you have. They will break up during the caramelizing step and be easier to "stuff" between the oatmeal slices. —ohyoucook
Line a loaf pan with plastic wrap; set aside. Cook oatmeal according to package directions, using 4 cups of water and 2 teaspoons salt. Let cool, then pack into prepared loaf pan. Cover and chill overnight.
The next morning, melt 1 tablespoon of the butter in a large skillet over medium-high heat. Add banana slices. Saute for 2-3 minutes or until golden browned. Sprinkle the brown sugar evenly over the bananas; saute another minute. Remove skillet from heat.
Turn oatmeal out of loaf pan onto cutting board; peel off plastic and cut into slices as thinly as possible. Spoon about 2 teaspoons of caramelized bananas down the center of half of the slices, then cover with remaining slices, sealing as best you can by gently pressing around the edges.
Return skillet to burner. Add remaining butter and melt over medium-high heat. Place 2 stuffed slices into the skillet. Fry until golden brown on each side. Transfer to a covered dish and keep warm. Repeat with remaining slices.
Garnish with a dollop of yogurt or whipped cream, chopped nuts and/or maple syrup, if desired, before serving.