Cook the orzo according to the package directions.
Meanwhile, in a bowl, combine the tomatoes, red pepper, 1 onion, basil, Feta, 2 tablespoons oil, vinegar, and ¼ teaspoon each salt and pepper. Set aside.
Heat the remaining oil in a large saucepan over medium heat. Add the garlic, chili flakes, and remaining onion. Cook until softened, about 3 minutes.
Add the beans, 3 cups broth, and lemon juice. Bring to a boil. Reduce heat to medium-low; simmer for 5 minutes. Remove from heat and let cool slightly.
Transfer the bean mixture to a food processor or blender. Pulse until combined but still slightly chunky. Season with ½ teaspoon salt and ¼ teaspoon pepper.
Return the bean mixture to a saucepan over medium heat. Add the remaining cup broth and bring to a simmer. Stir in orzo. Ladle soup into bowls and spoon salsa on top. Serve with bread (if desired).