Melt butter in a medium sized frying pan. Add brown sugar and bananas and cook over low heat for five minutes, stirring occasionally. Cool slightly.
Puree bananas (I use a hand blender, but you can do it in your regular blender). This makes about 1 ¼ cups of banana puree.
Pour puree into a measuring cup. Add enough milk to make 1 ¾ cups liquid. Pour into a large bowl and add pudding. Whisk until combined.
Fold about half of the whipped cream into the banana mixture. (If you like banana chunks in your pie, add some sliced bananas to your pie shell now.) Spread banana cream into cooled pie shell. Use remaining whipped cream to decorate the top of the pie. Store in refrigerator.