Sauté first 4 ingredients in 2 Tbsp. hot oil in a large Dutch oven over medium-high heat 3 to 5 minutes or until tender. Stir in broth and next 3 ingredients; bring to a boil, stirring occasionally. Reduce heat to medium, and simmer, stirring occasionally, 10 minutes.
Meanwhile, sprinkle chicken with salt and black pepper. Cook in remaining 1 Tbsp. hot oil in a large nonstick skillet over medium-high heat 5 minutes on each side or until lightly browned. Cool slightly (about 5 minutes); cut into 1-inch pieces.
Add okra, black-eyed peas, and chicken to Dutch oven. Simmer, stirring occasionally, 10 minutes or until okra is tender. Add tortellini, and cook, stirring occasionally, 3 minutes or until tortellini is done. Serve with Parmesan.