Preheat oven to 350°F (180°C). Grease a 9” x 5” (23 cm x 13 cm) loaf pan.
Combine bananas, yogurt and baking soda in a small bowl. Reserve.
Whisk egg, brown sugar, oil and vanilla in a medium bowl.
Add flour, baking powder and xanthan gum to a separate large bowl. Add reserved banana mixture and egg mixture to flour mixture. Stir together until flour is incorporated into batter.
Spoon batter into prepared pan. It will be very thick.
Bake in preheated oven for 70-75 minutes or until a toothpick inserted in center of cake comes out clean. Cool on wire cooling rack.
If top of cake starts to get too dark loosely place a piece of foil over the cake as it continues to bake.
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