Cut chiles in half lengthwise; remove stems and seeds. Place cut side down on a baking sheet. Roast for 15-20 minutes, until softened. Set aside. Combine broth and quinoa in a medium saucepan; bring to a boil. Cover, reduce heat, and simmer 15-18 minutes or until liquid is absorbed. Set aside.
In a small food processor, add the chipotle peppers with adobo sauce, and the tomato sauce. Process until smooth.
Add olive oil to a large nonstick skillet. Place over medium-high heat until hot. Add bell peppers, onion, green chilies, and garlic; saute 2 minutes. Remove from heat. Stir in quinoa, black beans, green onions, cilantro, lime juice, cumin, oregano and 2 Tbsp. of the sauce to the filling. Spoon the quinoa mixture into each chile half.
Pour several Tbsp. of the sauce into the bottom of a 9" x 13" casserole dish. Place stuffed chiles in dish. Top with remaining sauce. Cover and bake at 350 for 20 minutes. Sprinkle cheese over chiles; bake, uncovered, for an additional 10 minutes or until cheese melts and chiles are throughly heated.