For the bread: Preheat the oven to 350 degrees F. Spray a 9- by 5-inch loaf pan with cooking spray.
Whisk together the flour, baking soda, cinnamon and salt in a medium bowl.
Beat together the peanut butter, brown sugar and granulated sugar with an electric mixer on medium-high speed in a large bowl until smooth. Beat in the egg and vanilla, then fold in the mashed banana. Add the flour mixture, and beat on medium-low until just combined (it's OK if there are some lumps).
Transfer the batter to the prepared loaf pan, and bake until the bread is golden brown and has split at the top and a toothpick inserted in the center comes out clean, 1 hour 10 minutes to 1 hour 20 minutes. Run a knife around the edges, and let cool completely in the pan on a rack. (You can tent the bread with foil if it begins to brown too quickly.)
For the glaze: When the bread has cooled, combine the peanut butter, butter and confectioners' sugar in a medium microwave-safe bowl, and microwave in 30-second increments, stirring after each, until smooth. Let the glaze sit until it has stiffened up a bit but is still spreadable. Spread over the top of the bread, and sprinkle the peanuts on top. Let sit for 10 minutes to set up before slicing. The bread can be stored at room temperature in an airtight container for up to 3 days.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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