Begin by making the sugared pecans. Heat the vegetable oil in a deep pot over medium heat. Once hot, add the pecan halves and fry them for about 3–4 minutes, stirring frequently until they are golden brown. Remove them from the oil and drain on paper towels. While still warm, toss the pecans in confectioners sugar until evenly coated. Allow to cool completely.
In a large mixing bowl, combine the cake flour, baking powder, cinnamon, and salt. In another bowl, beat the softened butter and sugar together until light and fluffy. Gradually add the egg whites, mixing well after each addition. Then, mix in the mashed bananas and milk until fully incorporated.
Slowly add the dry ingredients to the banana mixture, stirring gently until just combined. Be careful not to overmix. Divide the batter evenly between the prepared cake pans and smooth the tops with a spatula. Bake at 350°F (175°C) for 25–30 minutes or until a toothpick inserted into the center comes out clean. Let the cakes cool in the pans for 10 minutes, then transfer to a cooling rack to cool completely.
In a double boiler or microwave, heat the heavy cream until it just begins to simmer. Remove it from the heat and add the chopped white chocolate, stirring until completely melted and smooth. Stir in the vanilla extract. Allow the ganache to cool slightly until it thickens to a spreadable consistency.
Once the cakes have cooled, place one layer on a serving plate. Spread a generous layer of white chocolate ganache on top, followed by the cooled sugared pecans. Add the second layer of cake and repeat the process by spreading more ganache on top and around the sides of the cake.
With the remaining ganache, create decorative swirls on top of the cake, and sprinkle any leftover sugared pecans for garnish. Chill the cake in the refrigerator for about 30 minutes to set the ganache before slicing and serving.