Preheat your oven to 350 degrees. Line a rimmed baking sheet with foil, covering the bottom and sides. Spray with nonstick cooking spray. Place a layer of matzo crackers on the sheet, breaking as needed to cover the sides; set aside.
In a heavy 2-quart saucepan, melt the butter over medium heat. Stir in the sugar and 2 tablespoons of water. Bring the mixture to a boil and cook undisturbed over medium-high heat until the caramel mixture is a light golden and registers 255 degrees on a candy thermometer, about 5-7 minutes. Remove from the heat and let cool for 1 minute. Stir in the vanilla and quickly pour over the matzos, using a metal spatula to spread evenly. Bake for 8 minutes.
Remove the bark from the oven and sprinkle with the chocolate chips. Return to the oven and bake just until the chocolate starts to melt, about 2 minutes, then spread the chocolate evenly.
Meanwhile, melt the peanut butter in a microwave safe bowl for 1-1 1/2 minutes, until it is a pourable consistency. Drizzle the peanut butter over the chocolate and, using the handle of a wooden spoon, swirl the chocolate and peanut butter together.
Let the bark cool for 1 hour, then refrigerate until set, at least 2 hours. Break into pieces and serve.