Cook the pasta according to the package instructions until al dente. Drain the pasta, reserving about 1/2 cup of the pasta water, and set it aside.
In a food processor or blender, combine the fresh basil leaves, grated Parmesan cheese, pine nuts (or walnuts), and garlic cloves. Pulse the ingredients until they form a coarse paste.
With the food processor still running, gradually add the extra-virgin olive oil in a steady stream until the mixture becomes smooth and creamy. If the pesto is too thick, you can add a little more olive oil to achieve the desired consistency.
In a large skillet over medium heat, add the pesto sauce and the heavy cream (or half-and-half). Stir the sauce until it is well combined and heated through. Season with salt and black pepper to taste.
Add the cooked pasta to the skillet with the creamy pesto sauce. Toss the pasta until it is evenly coated with the sauce. If the sauce is too thick, you can add a splash of the reserved pasta water to loosen it up.
Optional step: For added flavor and freshness, you can toss in some halved cherry tomatoes or extra grated Parmesan cheese at this stage.
Serve the Creamy Pesto Pasta immediately, garnishing with fresh basil leaves on top if desired.