In a large pot, cook the linguine according to the package instructions until al dente. Drain and set aside, reserving ½ cup of pasta water.
In a large skillet over medium heat, add 2 tablespoons of olive oil. Once hot, add the shrimp. Season with salt and pepper, and cook for 2–3 minutes until the shrimp are pink and opaque. Remove shrimp from pan and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant.
Add the halved cherry tomatoes and cook until they begin to soften, about 3–4 minutes. Stir in the fresh spinach and cook until wilted.
Reduce the heat to low and pour in the heavy cream, stirring to combine with the vegetables. Add the Parmesan cheese and Italian seasoning. Stir until the cheese is melted and the sauce is creamy.
Return the shrimp to the pan and mix well. If the sauce is too thick, gradually add reserved pasta water until you reach your desired consistency.
Toss the cooked linguine in the skillet with the creamy shrimp sauce until well coated. Adjust salt and pepper to taste.
Serve immediately, garnished with fresh basil leaves and more Parmesan cheese if desired.