Melt the butter in a large skillet over medium heat until it foams.
Whisk in the flour and cook for 30–60 seconds until lightly fragrant, forming a roux.
Slowly whisk in the chicken (or vegetable) broth until the mixture is smooth, then bring to a gentle simmer.
Gradually whisk in the heavy cream until fully combined, then simmer 2–3 minutes until slightly thickened.
Stir in the prepared pesto and grated Parmesan until the sauce is smooth and heated through.
Add the frozen or refrigerated tortellini directly to the sauce, stir to coat, and simmer 4–5 minutes (or until the tortellini is heated and tender).
Adjust seasoning if needed, garnish with chopped fresh basil, and serve immediately.