In a large pot, bring salted water to a boil. Add the refrigerated 3 cheese tortellini and cook according to package instructions until al dente (3-5 minutes). Reserve ½ cup of the pasta water, then drain and set aside.
In a large skillet over medium heat, melt the butter. Add the grated onion and sauté until translucent, about 3-4 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Sprinkle the flour over the sautéed onions and garlic, stirring constantly for about a minute to cook out the raw flour taste. Gradually whisk in the milk, ensuring there are no lumps, and bring the mixture to a simmer. Let it thicken slightly, stirring frequently.
Once the sauce has thickened, reduce the heat to low. Stir in the diced Neufchatel cheese and shredded parmesan cheese, mixing until the cheeses are melted and the sauce is smooth. Season with salt and freshly ground black pepper to taste.
Add the fresh or frozen spinach and chopped artichoke hearts to the sauce. If using frozen spinach, ensure it is thawed and drained. Cook for about 3-4 minutes until the spinach is wilted and everything is heated through.
Gently fold the cooked tortellini into the creamy mixture, adding reserved pasta water a little at a time until you reach your desired consistency. Stir to coat all the tortellini evenly with the sauce.
Remove from heat. Serve the Creamy Spinach Artichoke Tortellini in bowls, garnished with chopped fresh parsley if desired. Enjoy immediately!