Preheat the oven to 350 degrees F. Lightly brush a 9-by-5-by-3-inch loaf pan with butter.
Sift the flour, baking soda and salt into a medium bowl. Add the peanut butter and mix to combine. Whisk the vanilla and eggs together in a liquid measuring cup with a spout. Set aside.
In a stand mixer fitted with the paddle attachment or with an electric hand-held mixer, cream the butter and sugar until light and fluffy. Gradually pour in the egg mixture while beating; beat until incorporated. Mix in the bananas (the batter will appear curdled, but don't worry), then remove the bowl from the mixer. With a rubber spatula, fold in the flour mixture until just incorporated. Fold in 1/2 cup of the peanuts.
Add two-thirds of the batter to the prepared pan. Spread 1/2 cup of the strawberry preserves over the batter, making sure to leave a 1/2-inch border between the preserves and the sides of the loaf pan. Spread the remaining batter over the layer of preserves.
Bake until a toothpick inserted in the center of the bread comes out clean, about 55 minutes. Cool the bread in the pan on a wire rack for 5 minutes, then turn the bread out of the pan onto the rack. After it has cooled a bit but is still warm, spread the remaining 1/4 cup strawberry preserves over the top. Sprinkle with the remaining 1/4 cup chopped peanuts. Let cool completely before slicing and serving.