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Preheat oven to 350 degrees F.
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Using a 10 inch cast iron skillet, melt butter and stir in the brown sugar and salt. Cook over medium heat until the sugar and butter and salt are completely combined (1-2 minutes). Remove the pan from the heat.
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Cut the bananas in half crosswise and then slice the halves lengthwise into thirds. Arrange the banana slices (cut side down) on top of the butter/sugar mixture in the skillet.
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Set up your stand mixer with the paddle attached. Mix granulated sugar, brown sugar, and soft butter and mix (on high) until light and fluffy. This will take 3-5 minutes. Reduce the speed of your mixer to medium and mix in the eggs (one-by-one). Then, add the mashed bananas, sour cream (or yogurt), and vanilla extract. Mix until all ingredients are well-combined, scraping down the sides of the bowl with a spatula as necessary.
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In a separate medium bowl, whisk together the dry ingredients: flour, baking soda, baking powder, cardamom and salt. Slowly (and carefully) mix these dry ingredients into the stand mixer bowl with the wet ingredients. When these ingredients are well mixed, pour the batter over the caramel and bananas in the cast iron skillet. Smooth the top.
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Set the skillet on a rimmed baking sheet and bake at 350 degrees F. until the cake is lightly browned and a toothpick comes out clean when inserted into the middle of the cake. This will bake 40-45 minutes.
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Remove cake from oven and cool completely. When the cake is totally cool, run a butter knife around the edge of the cake. Then, set the skillet back on the stovetop over very low heat and warm the cake until it is just barely warm on the bottom (about 2 minutes). Remove the skillet from the heat and carefully invert the cake onto your serving platter.
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Serve garnished with chopped walnuts and a scoop of high quality vanilla ice cream. (Why not try the vanilla ice cream recipe on Blue Cayenne? It is delicious and easy to make.)