Bring a large pot of water to a boil. Add a little salt and the radiatori pasta. Cook pasta until al dente, following the package directions. Drain the pasta and set aside.

Heat 2 teaspoons of olive oil in a large skillet over medium heat. Add the sliced zucchini, seasoning lightly with salt and pepper. Sauté for 4-5 minutes, stirring occasionally, until tender. Remove and set aside with pasta.

Add another 1 teaspoon of olive oil to the same large pan. Increase to medium high heat. Add the shrimp in a single layer and season with salt and black pepper. Cook for 2-3 minutes per side, until pink and opaque. Remove shrimp and set aside with the zucchini and pasta.

Add the last teaspoon of oil to the skillet, still on medium high heat. Stir in the minced garlic and cook until fragrant, about 30 seconds. Toss in the cherry tomatoes and chicken broth and cook for 3-5 minutes, until they begin to burst and peel.

Return the cooked pasta, zucchini, and shrimp to the pan. Add 1/2 cup freshly grated parmesan and toss until everything is evenly coated.

To serve, top with fresh chopped basil and more parmesan cheese, if desired.