Make the mint chutney: In a medium bowl, soak the split chickpeas in 4 cups of water for 30 minutes. Drain the chickpeas and set aside.
While the chickpeas are soaking, in a small sauté pan over low heat, warm the oil. Add the mint, onion, green chiles, and garlic and sauté, stirring occasionally, for 3 minutes. Remove the pan from the heat and let the mixture cool. Transfer to a blender, add the tamarind paste and salt along with the soaked chickpeas and 1/2 cup water and blend to make a paste.
Make the lentil soup: In a large saucepan over moderate heat, combine the red lentils, spinach, onion, and salt and cook for 10 minutes. Add the 6 cups of water, reduce heat to low, and simmer for 20 minutes.
While the soup is simmering, in a small sauté pan over low heat, warm the oil. Add the green chiles, mustard seed, crushed red pepper, turmeric, and cumin seeds and toast, stirring, until the mustard seeds pop, about 2 minutes. Stir the spice mixture into the soup, divide the soup among bowls, and top with the mint chutney.