In a large pot, bring salted water to a boil. Add the linguine pasta and cook according to the package instructions until al dente. Once cooked, drain the pasta and set aside, remembering to reserve ½ cup of the pasta water for later use.
In a large skillet, heat 2 tablespoons of olive oil over medium heat. When the oil is hot, add the peeled and deveined shrimp. Season generously with salt and pepper. Sauté the shrimp for 2 to 3 minutes or until they turn pink and opaque. Carefully remove the shrimp from the skillet and set them aside on a plate.
Using the same skillet (add a bit more oil if necessary), add the minced garlic. Sauté for approximately 30 seconds or until fragrant, taking care not to burn it.
Toss in the halved cherry tomatoes and cook for about 3 to 4 minutes, or until they start to soften. Fold in the fresh spinach and continue cooking until it's wilted, stirring occasionally to promote even cooking.
Lower the heat to a gentle simmer. Pour in the heavy cream and stir together with the sautéed vegetables. Next, add the grated Parmesan cheese and Italian seasoning, stirring until the cheese is completely melted and the sauce becomes luscious and creamy.
Return the sautéed shrimp to the pan, mixing well to coat them in the sauce. If the sauce appears too thick, gradually add the reserved pasta water a little at a time until you achieve your desired creamy consistency.
Gently toss the cooked linguine into the skillet with the creamy shrimp sauce. Ensure that every strand of pasta is well coated with the rich mixture. Taste and adjust salt and pepper as needed.
Plate the pasta immediately, garnishing with fresh basil leaves and an extra sprinkle of Parmesan cheese, if desired.