Preheat oven to 350°F (180°C).

In a 10-inch cast-iron skillet, melt 1⁄3 cup (76 grams) butter over medium heat. Whisk in brown sugar, and cook, stirring occasionally, until mixture starts to caramelize, 4 to 5 minutes. Slowly whisk in lemon juice until combined. Remove from heat. Place banana halves, cut side down, on top of caramel, cutting bananas to fit, if necessary.

In the bowl of a stand mixer fitted with the paddle attachment, beat granulated sugar and remaining 1⁄2 cup (113 grams) butter at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in peanut butter and vanilla until combined.

In a medium bowl, stir together flour, baking powder, baking soda, and salt. With mixer on low speed, gradually add flour mixture to butter mixture alternately with milk, beginning and ending with flour mixture, beating just until combined after each addition. Carefully spoon batter over bananas in skillet, smoothing top with an offset spatula.

Bake until a wooden pick inserted in center comes out clean and an instant- read thermometer inserted in center registers 205°F (96°C), 45 to 50 minutes. Let cool in skillet for 10 minutes. Carefully invert cake onto a rimmed serving plate. Serve warm or at room temperature. Refrigerate in an airtight container for up to 2 days.