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 cook until the tortellini float, about 3 minutes; they should reach 165°F internally.
Drain the cooked tortellini completely in a colander and set aside.
While the tortellini cook, whisk the remaining 1 1/2 cups broth together with the cornstarch until smooth.
Melt the butter in a large non-stick skillet over medium-high heat until it foams, then 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 drained tortellini to the skillet and toss gently to coat them evenly with the garlic-butter sauce.
Transfer to a serving dish and garnish with freshly grated Parmesan and chiffonaded basil, if using.