Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking dish with butter and lightly dust with flour.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, and ground cinnamon. Set aside.
In a large bowl, combine the mashed bananas, granulated sugar, and melted butter. Mix well.
Add the eggs one at a time to the banana mixture, beating well after each addition. Stir in the vanilla extract.
Alternately add the dry ingredients and buttermilk to the banana mixture, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter into the prepared baking dish and smooth the top with a spatula.
Bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 15 minutes.
While the cake is cooling, prepare the tres leches milk mixture by combining the whole milk, sweetened condensed milk, and evaporated milk in a bowl. Stir until well combined.
Using a fork or skewer, poke holes all over the surface of the warm cake to allow the milk mixture to soak in.
Slowly pour the tres leches milk mixture evenly over the cake, allowing it to absorb fully.
Refrigerate the cake for at least 4 hours or overnight to let the flavors meld and the cake become moist.
Before serving, prepare the whipped cream topping by whipping the heavy cream, powdered sugar, and vanilla extract together until stiff peaks form.
Spread the whipped cream evenly over the soaked cake.
Slice and serve chilled.