Bananas Foster originated at Brennan's restaurant in New Orleans in the 1950s. This is a gluten-free riff on that classic dessert.
Preheat oven to 350°.
Line a 9-inch square metal baking pan with foil, allowing foil to extend over edge of pan; coat foil with cooking spray.
Weigh or lightly spoon flours and potato starch into dry measuring cups; level with a knife. Combine flours, potato starch, baking powder, xanthan gum, and cinnamon in a medium bowl; stir with a whisk.
Place brown sugar and 3 tablespoons butter in a small saucepan. Cook over low heat 2 minutes or until butter melts and mixture is smooth, stirring constantly. Pour into prepared pan, spreading evenly. Sprinkle with pecans.
Cut each banana in half crosswise; cut each half lengthwise into 1/8-inch-thick slices. Arrange banana slices over pecans in pan.
Place granulated sugar and 3 tablespoons butter in a large bowl; beat with a mixer at medium speed until light and fluffy. Add eggs, 1 at a time, beating well after each addition. Beat in milk, yogurt, rum, and vanilla until well blended. Gradually add flour mixture, beating at low speed until smooth. Pour batter over bananas in pan. Bake at 350° for 45 minutes or until a wooden pick inserted in center comes out clean. Cool 10 minutes in pan. Place a plate upside down on top of cake; invert onto plate. Serve warm.