Position a broiler pan on the rack closest to the broiler element and preheat to high.
For the chutney: With the machine running, drop the ginger into the bowl of a food processor and process until coarsely chopped. Scrape down the sides of the bowl, then add the scallions, mint, cilantro, yogurt, jalapeno, lime juice, and salt. Process to a textured sauce similar in consistency to pesto, adding water to adjust the consistency, if necessary. Transfer to a bowl and set aside.
For the fish: rub the oil, curry, salt and pepper on the fish. Carefully lay the swordfish on the preheated broiler pan and return to the broiler. Cook the steaks without turning until just cooked through more or until an instant-read thermometer inserted in the side registers about 135 degrees F, about 4 minutes. Transfer steaks to 4 plates and serve with the chutney and rice, if desired.
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