Cook the Pasta: Bring a large pot of water to a boil, add 1 tablespoon of rock salt and dissolve. Add fusilli pasta and cook according to package instructions, stirring occasionally.
Prepare the Cherry Tomatoes: Cut the cherry tomatoes in half, squeezing each half gently to release the juice. Press down on them with a spoon to extract as much juice as possible.
Season the Tomatoes: Add a pinch of salt, a generous amount of pepper, and a good amount of extra virgin olive oil to the tomatoes. Mix well.
Add Basil: Tear the basil leaves by hand and add them to the tomato mixture. Mix together and set aside.
Cool the Pasta: Once the pasta is al dente, strain and transfer to a separate mixing bowl or tray to cool down. Drizzle with extra virgin olive oil and toss to coat evenly.
Combine Ingredients: Add the sun-dried tomatoes, crushed black olives, and tuna to the tomato mixture. Mix well. Once the pasta has cooled, add it to the mixture.
Finish the Salad: Pour in more extra virgin olive oil if needed and mix well. Gradually add the Provolone cubes as you continue to mix. If the mixture appears dry, add more EVOO.
Serve: Serve the pasta salad at room temperature. Optionally, finish with more shaved Parmigiano Reggiano on top.