Bring 2 1/2 cups of the broth to a boil in a large pot or Dutch oven.
Add the frozen cheese tortellini to the boiling broth and return to a boil; cook until the tortellini float, about 3 minutes, or until the internal temperature reaches 165°F. Drain completely in a colander.
Meanwhile, whisk the remaining 1 1/2 cups broth with 2 tablespoons cornstarch until smooth.
In a large nonstick skillet over medium-high heat, melt 4 tablespoons butter until foaming. Add the minced garlic and dried basil and cook, stirring, for about 2 minutes.
Stir the broth–cornstarch mixture into the skillet, bring to a boil, and simmer until the sauce thickens, about 2 minutes.
Add the cooked tortellini to the skillet and toss gently to coat evenly with the sauce.
Transfer to a serving dish and garnish with freshly grated Parmesan and chiffonaded basil, if using.