Melt the butter in a large skillet over medium heat until foaming.
Whisk in the flour and cook, whisking constantly, for 30–60 seconds to form a roux.
Slowly whisk in the broth until smooth, then bring the mixture to a gentle simmer.
Whisk in the heavy cream gradually until combined, bring back to a simmer, and cook 2–3 minutes to thicken slightly.
Stir in the pesto and grated Parmesan until the sauce is smooth.
Add the frozen or refrigerated tortellini directly to the sauce, stir to coat, and simmer 4–5 minutes or until the tortellini are heated through and tender.
Remove from heat, garnish with chopped fresh basil, and serve immediately.