Warm milk and butter in a small pot on the stove or microwave until it's 110 degrees F. Make sure it isn't too hot and it should feel like warm bath water. I highly recommend using a food thermometer. Add the milk mixture and yeast to the bowl of a stand mixer and whisk together until combined and the milk is frothy. Let sit for 2 minutes. Add sugar, eggs, vanilla extract and mashed banana. Mix until well combined.
Add 3 3/4 cups flour and cinnamon to the dough and mix in with a wooden spoon until dough begins to form. Place the mixing bowl on the stand mixer and knead the dough with a dough hook for about 8 minutes until a dough ball is formed, scrape down the sides of the bowl a few times. The dough will be slightly sticky but shouldn't stick to your hands. If it is too sticky add 2 tablespoons of flour at a time. If you don't have a stand mixer you could use your hands and knead the dough on a well-floured surface.
Transfer the dough ball to a lightly greased bowl, cover with a warm damp towel and let dough rise for an 1 – 1 1/2 hours, or until it has doubled in size. The time will vary depending on the humidity and temperature in your home. To make your towel warm, place the damp towel in the microwave for 30 seconds
After the dough has doubled in size, transfer to a lightly floured surface and roll out to about 16×12 inch rectangle. Mix the softened butter, brown sugar and cinnamon in a small bowl and mix with a fork until combined. Then spread the mixture over the dough, covering every inch. Then cover with banana slices.
Lightly grease a 13 x 9 inch baking dish or line with parchment paper. With a pizza cutter or sharp knife, cut into 12 strips from the longer side dough. Roll into a cinnamon roll and place on the prepared baking dish. Cover the rolls again and place a warm damp towel on top. Let rise for another 30-45 minutes. They will get a little puffy and rise a bit.
Preheat oven to 350 degrees F. Bake cinnamon rolls for 30-32 minutes or until just slightly golden brown on the edges. You want to under-bake them a little so they stay soft and gooey in the middle.
While the cinnamon rolls are cooling, add all of the frosting ingredients together and beat with an electric mixer or whisk until smooth, light and fluffy. Spread the frosting over warm Banana Cinnamon Rolls and serve immediately. Top with chopped walnuts and more banana slices optional, enjoy!