In a medium saucepan combine broth, farro, and water. Bring to boiling. Reduce heat, cover, and simmer about 30 minutes or until farro is tender. Drain farro, reserving 1/2 cup of the cooking liquid; set both the farro and cooking liquid aside.
Preheat oven to 400 degrees F. Remove husks from the ears of corn. Scrub with a stiff brush to remove silks; rinse.Cut corn from cobs; set corn aside, discarding cobs. In a large skillet melt the butter over medium heat. Stir in curry powder. Add reserved corn and green onions. Cook for 2 minutes, stirring occasionally. Add squash and cook for 2 minutes more. Stir in reserved farro, salt, and black pepper; cool slightly. Stir in 1/2 of the cheese and 1/2 of the basil.
Cut sweet peppers in half lengthwise. Remove and discard seeds and membranes from the peppers. Fill pepper halves with farro mixture. Place stuffed peppers in a 3-quart rectangular baking dish. Pour the reserved cooking liquid into dish around the peppers. Cover dish with foil. Bake for 30 minutes. Remove foil. Sprinkle with remaining cheese. Bake, uncovered, about 15 minutes more or until peppers are crisp-tender and cheese is melted. Sprinkle with remaining basil.