Preheat the oven to 350 degrees F (175 degrees C). Grease a 9×5-inch loaf pan.
Whisk together flour, baking powder, and baking soda in a medium bowl. Combine bananas and cream in another bowl.
Cream sugar and butter in a third bowl with an electric mixer until light and fluffy. Beat in egg. Add flour mixture in 2 batches, alternating with the banana mixture, beating batter briefly after each addition. Fold in chocolate chips and pecans. Pour batter into the prepared pan.
Place chocolate-hazelnut spread in a microwave-safe bowl. Microwave on High until melted, about 25 seconds. Pour over the batter in the pan and swirl in with a knife.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 60 to 70 minutes.
While the bread is baking, whisk the brown sugar, half-and-half, butter, and salt in a saucepan over medium-low heat until it thickens, 5 to 7 minutes. Add vanilla and cook until a bit thicker, about 1 minute. Remove from heat and cool slightly. Pour sauce into a jar and refrigerate until cold.
Cool the bread in the pan for 10 minutes before removing to a wire rack to cool completely. Serve with caramel sauce.
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