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Bring a large pot of water to a boil. Add butternut squash and let cook until tender, about 15 minutes. Drain and return to the pan. Add 1 ½ teaspoons chile powder and salt. Mash until almost smooth.
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Meanwhile, combine beans, green onions, lime juice, cumin and the remaining ½ teaspoon chile powder in a mixing bowl bowl.
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Spread about ¼ cup mashed squash on each tostada. Top each with about 3 tablespoons of the bean mixture, ¼ cup lettuce and 1 tablespoon cheese.