Preheat an oven to 180 degrees C. Spray an oblong baking dish with cooking spray.
Break matzo sheets in half and run under warm water to soften. Pour tomato puree into bowl and season with salt and pepper. Coat the bottom of the prepared baking dish with some of the tomato puree then begin layering with the softened matzo sheet, Swiss cheese, mozzarella cheese and tomato puree. Continue layering until the cheeses are used up, finishing with a layer of matzo. Top with the remaining tomato puree and sprinkle with Parmesan cheese and oregano.