Place chickpeas and kidney beans into a large container; cover with several inches of cool water. Let stand 8 hours to overnight; drain.
Heat 1 tablespoon olive oil in a skillet over medium heat. Add red onion; cook and stir until onion has softened and turned translucent, about 5 minutes. Reduce heat to low; continue cooking and stirring until onion is tender and golden brown, about 40 minutes more. Stir in dried mint; cook until onions become dark brown and crisp, about 15 minutes. Set aside for garnish.
Heat remaining olive oil in a stock pot; stir in yellow onions. Cook and stir until onion has turned translucent, about 5 minutes. Add garlic and stir until fragrant, about 1 minute. Stir in chickpeas, kidney beans, and turmeric; toss to combine. Stir in vegetable stock; simmer soup for 1 hour.
Stir scallions, parsley, cilantro, mint, and lentils into soup; simmer 30 minutes more. Break linguine into 3 sections, stir into soup, and cook at a low boil until noodles are soft, 8 to 10 minutes.
Stir 1/2 of the spinach into the soup until wilted, about 1 minute. Stir in remaining spinach and simmer for 30 minutes, stirring occasionally.
Stir flour with 3 tablespoons of the soup liquid together in a small bowl until smooth. Stir flour mixture back into soup. Continue to simmer soup over low heat, stirring frequently, until thickened, about 30 minutes.
Serve soup with yogurt and fried red onions.
Cook's Notes:
Save time by frying the onions while the soup is simmering.
It is important to stir gently and often toward the end of the cooking process, or soup will stick to the bottom of the pot. Add more water or stock as needed to prevent sticking.
