Bring a large pot of salted water to a boil and cook the cheese tortellini according to package directions; drain and set aside.
In a medium saucepan over medium heat, melt the butter. Add the minced garlic and cook, stirring, for about 1 minute until fragrant.
Add the all-purpose flour to the butter and garlic, stirring constantly and cook for 1 minute to form a roux.
Gradually whisk in the milk and chicken broth, stirring constantly. Continue to cook and stir until the sauce comes to a boil and thickens slightly.
Stir in the grated Parmesan until melted. Season with salt and pepper to taste.
Add the cooked tortellini to the sauce and gently toss until evenly coated.
Serve immediately, sprinkled with the chopped fresh parsley.