Heat the oil in a large skillet over medium-high heat. Add the eggplant, bell peppers, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Cook, stirring occasionally, until the vegetables begin to soften, 6 to 8 minutes.
Add the garlic and red pepper flakes and cook, stirring, for 1 minute.
Add the broth and tortellini. Cover and simmer over medium heat, stirring occasionally, until the tortellini are cooked through and most of the broth is absorbed, 12 to 15 minutes.
Fold in the parsley and 1/4 cup of the Parmesan. Spoon into bowls and sprinkle with the remaining 1/4 cup of Parmesan.