Add the onions to a microwave safe bowl and cook them in the microwave for 3-4 minutes to soften. In a large nonstick soup pot or pan, heat 1 tablespoon oil. Add tomatoes, ½ of the cooked onions, Ortega chilies, garlic, and ½ teaspoon cumin. Sauté over medium heat for 10 minutes. Stir often.
Add 2 cups broth and tortillas; simmer 20 minutes. Stir often. Transfer mixture to a blender and purée. Set aside.
In the same large, nonstick pot or pan, heat 1 teaspoon oil. Add the remaining cooked onions, paprika, chili powder, 1½ teaspoon cumin, red pepper flakes, ¼ teaspoon salt and black pepper. Cook for 2 minutes. Stir often.
Mix in 3 cups broth, cooked chicken, black beans, hominy, and pureed mixture from the blender; simmer 10 minutes.
To serve: Ladle 1¾ cups into each bowl. Stir in ¼ cup romaine lettuce, if desired.