In a large skillet over medium heat, melt the butter until foaming.
Whisk in the flour and cook, stirring, for 30–60 seconds to make a roux.
Slowly whisk in the chicken (or vegetable) broth until smooth, then bring the mixture to a gentle simmer.
Gradually whisk in the heavy cream until fully combined, then return to a simmer and cook for 2–3 minutes to thicken slightly.
Stir in the pesto and grated Parmesan until the sauce is smooth and homogeneous.
Add the frozen or refrigerated tortellini directly to the sauce, stir to coat, then simmer for 4–5 minutes (or until heated through and tender).
Remove from heat, garnish with chopped fresh basil, and serve immediately.