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Preheat oven to 400°.
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Toss butternut squash cubes with ½ tablespoon of oil until evenly coated. Arrange in an even layer on baking sheet. Bake 20 minutes, flipping about halfway through. Remove from oven and allow to cool for a few minutes.
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Place cooked butternut squash into food processor bowl, along with beans, panko, curry paste, scallions and salt. Blend briefly, just until completely mixed, stopping to scape down sides of bowl as needed. Shape into 4 patties.
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Coat a large skillet with remaining oil and place over medium heat. Working in batches if necessary, arrange patties on skillet. Cook until browned on bottoms, about 5 minutes, flip and cook until browned on opposite sides, about 5 minutes more. Add a bit more oil to skillet between batches if it becomes too dry.