Preheat oven to 350°F. Melt 1/4 cup of the butter in a 10-inch cast-iron skillet over low; stir in rum. Sprinkle brown sugar evenly over butter mixture. Remove from heat.
Cut bananas in half crosswise; cut each half lengthwise into 3 slices. Arrange banana slices in a spoke pattern over brown sugar mixture. Sprinkle pecans evenly over bananas and brown sugar mixture.
Beat together 1/2 cup of the granulated sugar and remaining 1/4 cup butter in a large bowl with an electric mixer at medium speed until blended. Add egg yolks, 1 at a time, beating just until blended after each addition, reserving egg whites for later. Add buttermilk and vanilla, beating just until blended. Add pancake mix and cinnamon, beating just until blended.
Beat egg whites in a medium bowl with an electric mixer until soft peaks form. Gradually beat in remaining 1/4 cup granulated sugar until stiff peaks form. Fold into batter.
Spread batter evenly over pecans and bananas in skillet. Place skillet on a rimmed baking sheet. Bake in preheated oven until a wooden pick inserted in center comes out clean, 40 to 45 minutes. Cool in skillet on a wire rack 10 minutes. Invert cake onto a serving plate. Serve warm.
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