Fill a large pot with lightly salted water and bring to a rolling boil; stir in tortellini and return to a boil. Cook uncovered, stirring occasionally, until the tortellini float to the top and the filling is hot, 3 to 5 minutes. Drain and set aside.

Heat butter and olive oil in a large saucepan over medium-low heat. Add broccoli, red bell pepper, yellow bell pepper, green onions, and garlic; cook until crisp-tender, 3 to 4 minutes. Pour in chicken broth and bring to a simmer.

Combine half-and-half and cornstarch in a bowl; add to broth mixture. Cook until sauce has slightly thickened, 5 to 7 minutes. Add basil, oregano, and red pepper flakes and mix well.

Pour sauce over cooked tortellini and toss to coat. Top with Parmesan cheese, salt, and pepper.