Combine Wet Ingredients: In a medium bowl, whisk together the egg and granulated sugar until the mixture becomes light and fluffy. Gradually incorporate the milk, salt, and vanilla extract, stirring until well combined.

Incorporate Dry Ingredients: In a separate bowl, whisk together the cake flour and baking powder. Gradually add the dry ingredients to the wet ingredients, gently folding until just combined. Overmixing can result in a tough cake.

Create a Smooth Batter: Stir in the cooking oil until the batter reaches a smooth consistency.

Prepare the Pan: Place the frying pan over low heat. Add the unsalted butter and allow it to melt evenly.

Create a Sweet Base: Sprinkle the unrefined sugar over the melted butter. Once the sugar begins to caramelize, distribute the banana slices evenly over the caramelized sugar.

Pour Batter: Carefully pour the prepared batter over the bananas in the frying pan.

Cover and Cook: Place a lid on the frying pan and cook over low heat for approximately 25 minutes, or until the cake is cooked through and the bottom is golden brown.

Monitor Cooking: Periodically check the cake's progress. If the cooking sounds excessive, reduce the heat. Conversely, if there's little to no activity, increase the heat slightly.

Invert Carefully: Once the cake is cooked, carefully invert the frying pan onto a plate to release the cake.

Adjust Appearance: If desired, return the cake to the pan and cook the other side for a few minutes to achieve a desired caramelization.

Serve Warm: Allow the cake to cool slightly before serving.