Preheat a convection oven to 350° F to 400° F (180° C to 200° C). Place a shrimp on one square of pasta, roll it up with the tail sticking out, and place it in a baking pan seam-side down so the roll stays closed.
Repeat with the remaining shrimp and pasta, wedging the shrimp together in the pan. Pour the broth over the shrimp, sprinkle on the cheese, season with pepper, sprinkle with parsley, and drizzle with a little olive oil.
Bake until the surface is browned, about 10 minutes. Serve immediately.