Pulse the tomatoes, with their juice, in a food processor until mostly smooth, about 8 pulses.
Heat 2 tablespoons of the oil in a large Dutch oven over medium-high heat until shimmering. Add the curry powders and garam masala, and cook until fragrant, about 10 seconds. Add the onions, yam and potato and cook, stirring occasionally, until the onions are browned and the vegetables are softened slightly, about 7 minutes. Reduce the heat to medium. Clear the center of the pot, stir in the remaining 1 tablespoon oil, garlic, ginger, tomato paste, and chile, and cook about 30 seconds. Add the cauliflower and cook, stirring occasionally, until the spices coat the florets, about 2 minutes.
Stir in the processed tomatoes, water, chickpeas, and ½ teaspoon salt, scraping up any browned bits. Bring to a simmer, cover and cook, stirring occasionally, until the vegetables are tender, about 15 minutes.
Stir in the peas and continue to cook until heated through, about 2 minutes longer. Off the heat, stir in the yogurt. Serve over rice with cilantro, cashews and green onions for garnish.