Methods

1. Using a fork smash the 3 overripe bananas in a medium bowl. Microwave the bananas for a minute on high heat and then transfer the fruit into a fine mesh strainer and sit over a bowl to drain the liquid for 1 hour. Avoid the temptation to press the pulp. Discard the liquid. Cool the pulp completely to room temperature before using.
2. Preheat the oven to 325F.
3. Grease and line a circular 9-inch baking pan with 2 Tbsp ghee and parchment paper.
4. Slice the remaining two ripe bananas across their length and spread the slices on the surface of the prepared baking pan to cover the entire area. Keep aside.
5. In a small saucepan, heat the 1/4 cup of the sugar, cream of tartar and water on medium-high heat until the sugar just starts to caramelize and starts to turn a light amber color. Drizzle the hot liquid over the sliced bananas in the pan, followed by the maple syrup. Keep aside.
6. In a medium bowl dry whisk the flour, cardamom, baking powder, baking soda and salt and keep aside. 
7. In the bowl of a stand mixer, cream the butter, 2 Tbsp ghee and remaining 1/2 cup of sugar on medium-high speed for about 3 to 4 minutes using the paddle attachment, until light and fluffy. Then whisk in one egg at a time, until combined. Scrape the sides of the bowl. Add half of the sifted dry ingredients to the bowl and mix on low-speed until just combined. Then add the cooled, drained banana pulp to the batter and remaining sifted dry ingredients and whisk until combined and no visible flecks of flour remain.
8. Transfer the batter to the cake pan and spread it evenly using an offset spatula. Bake in the preheated oven for about 50 to 60 minutes or until a skewer comes out clean from the center. Once baked remove the pan from the oven and allow to cool for 10 minutes in the pan over a wire rack.
9. To release the cake, run a knife around the edges of the cake and then place a serving plate over the baking dish, then carefully invert the cake over the plate and remove the pan. Peel the parchment paper off.
10. Serve the cake warm with a little bit of creme fraiche on the side.