Heat ¼ cup vegetable oil in 12-inch nonstick skillet over medium heat until shimmering. Add 2 large onions, halved and sliced thin through root end and ¼ teaspoon table salt, and cook, stirring frequently, until onions are translucent, about 2 minutes. Add ¾ teaspoon turmeric and continue to cook, stirring frequently, until onions are deep golden brown and caramelized, about 25 minutes. Transfer to bowl and set aside. Wipe out skillet with paper towels and set skillet aside.

Combine 8 cups vegetable broth, 2 cups water, 1 cup dried green lentils, rinsed, and remaining 1½ teaspoons salt in Dutch oven and bring to boil over high heat. Reduce heat to medium-low, cover, and simmer for 15 minutes, stirring occasionally and adjusting heat as needed to maintain simmer. Stir in 1 rinsed can chickpeas and 1 rinsed can red kidney beans and simmer, covered, until lentils are tender, about 15 minutes, adjusting heat as needed.

Meanwhile, in now-empty skillet, heat 2 tablespoons oil over medium heat until shimmering. Add 3 tablespoons minced garlic and ¼ teaspoon turmeric and cook, stirring frequently, until garlic is just beginning to turn golden brown, about 2 minutes. Transfer garlic and oil to second bowl and set aside. Wipe out skillet with paper towels. Add remaining ¼ cup oil to again-empty skillet and heat over medium heat until shimmering. Add 3 tablespoons dried mint and cook, stirring frequently, until fragrant and just beginning to brown, about 1 minute. Transfer to third bowl and set aside.

Stir half of reserved caramelized onions, half of reserved browned garlic, 12 ounces frozen chopped spinach, thawed and squeezed dry; 1½ cups thinly sliced scallions, 1 cup chopped fresh parsley leaves and tender stems, 1 cup chopped fresh cilantro leaves and tender stems, remaining 2 teaspoons turmeric, and 1 teaspoon pepper into pot with bean mixture. Cover pot and bring to boil over high heat. Reduce heat to medium-low and cook, stirring occasionally, until greens, lentils, and beans are uniformly tender and stew has thickened, about 30 minutes.

Stir 3 ounces reshteh, broken in half, into pot and cook, uncovered, until pasta is tender, about 15 minutes, stirring occasionally. Remove pot from heat and let sit until stew is thickened slightly, about 15 minutes. Season with salt to taste. Add water to ½ cup kashk in bowl, 1 tablespoon at a time, until it is the consistency of heavy cream. Serve soup, topping individual portions with remaining reserved caramelized onions, remaining reserved browned garlic, reserved mint oil, and thinned kashk.