Melt the butter in a 10-inch cast-iron skillet over medium heat. Add the brown sugar and salt and cook until melted, stirring occasionally.
Transfer the warm caramel to the bottom of a baking pan and decoratively press the bananas (flat side down, rounded side up) into the caramel, until all of the caramel is topped with bananas. Set aside.
Whisk the flour, baking powder, and salt in a medium-sized bowl, and set aside.
Place the oil, sugar, and vanilla in a large bowl. Whisk to combine. Add the egg and yolk, and continue whisking until smooth. Add the buttermilk and whisk again.
Add the dry ingredients to the wet, and using a rubber spatula, gently fold to combine. Do not over mix.
Scrape the batter over the bananas and gently smooth the top. Bake for 35 to 40 minutes, rotating at the halfway point until a cake tester comes out with a moist crumb or two. Immediately run a paring knife around the edge of the pan. Let sit for 5 minutes, then carefully invert the cake onto a serving platter. If bits of caramel or banana stick to the bottom of the pan, scrape them off and place them back onto the cake. Let cool until the caramel sets a bit, about 20 minutes, or cool to room temperature. Serve with vanilla ice cream or whipped cream.
Serving Size 1 cake, 8 slices