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. Remove from the heat 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.
The cake will keep wrapped in plastic on the counter for up to 3 days, but it is best the day it is made.
Jessie Sheehan is a cookbook author, food writer, recipe developer, and baker. She is the author of The Vintage Baker and the co-author of Icebox Cakes (both published by Chronicle Books). She has developed recipes for many cookbooks, besides her own, and has contributed recipes/and or written for Better Homes & Gardens, Rachael Ray Everyday, The Washington Post, Epicurious, Food52, Fine Cooking, TASTE, Chowhound, The Spruce Eats, Little Sous, and Main Street Magazine, among others. She blogs at jessie sheehan bakes and can be found on Instagram at @jessiesheehanbakes. She likes layer cakes with lots of frosting and cookies that are thick and chewy. Oh, and she has a soft spot for chocolate pudding. She lives in Red Hook, Brooklyn, with her husband and two boys, not far from her beloved Baked, the bakery where she got her start.