Preheat the oven to 350 degrees F. Lightly butter a 13 by-9-inch baking pan.
Put 2 cups milk, the eggs, peanut butter, sugar, vanilla, and salt into a blender and blend until smooth, taking care that the peanut butter is thoroughly emulsified into the mixture. Pour into a large bowl, then whisk in the remaining 2 cups milk. Stir in the bread and set aside to soak for about 10 minutes. Pour this mixture into the prepared baking pan. Place spoonfuls of your favorite jelly, jam, or preserves around the bread mixture, pushing them in a bit with your spoon. Bake for about 45 minutes, or until the pudding is browned, puffed, and a little firm. Let cool. Cut into squares to serve.