In a large pot, bring salted water to a boil. Add the cheese tortellini and cook according to the package instructions until al dente. Drain the tortellini and set it aside, reserving a little pasta water in case you need to thin the sauce later.
In a skillet over medium heat, melt the butter. Once melted, add in the flour and whisk continuously for about 1 minute, until the mixture is bubbly and golden.
Gradually pour in the heavy cream and chicken or vegetable broth, whisking constantly to prevent lumps. Bring the mixture to a gentle simmer.
Once the sauce is thickened, stir in the pesto and grated parmesan cheese. Mix well until the cheese is melted and the sauce is creamy.
Add the cooked tortellini to the sauce, gently tossing to coat the pasta evenly. If the sauce is too thick, add a little reserved pasta water until you reach your desired consistency.
Remove from heat and garnish with chopped fresh basil before serving. Enjoy your Creamy Pesto Tortellini warm!