Position a rack in the middle of the oven and preheat to 350 degrees . Line a rimmed baking sheet with foil, covering the bottom and sides. Place a layer of matzo crackers on the sheet, breaking as needed to cover the surface; set aside.
In a heavy 2-quart saucepan, melt the butter over medium heat. Stir in the sugar and 2 tablespoons water. Bring the mixture to a boil over medium-high heat and cook undisturbed until the caramel mixture is light golden and registers 255 degrees on a candy thermometer, 5 to 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 brittle from the oven and sprinkle with the chocolate chips. Bake just until the chocolate starts to melt, about 2 minutes, then spread the chocolate evenly and let the brittle cool for 5 minutes.
Meanwhile, melt the peanut butter in the saucepan over low heat; drizzle across the chocolate and, using the handle of a spoon, swirl the chocolate and peanut butter. Sprinkle with salt.
Let the brittle cool for 1 hour, then refrigerate until set, at least 2 hours. Break into pieces to serve.