8 individual baby winter squash (such as sweet dumpling) or four 1½-pound acorn squash
2 tablespoons extra-virgin oil plus additional for brushing
1 teaspoon coarse kosher salt plus additional for sprinkling
10 cups ½-inch cubes peeled seeded butternut squash (from 4½ pounds)
4 tablespoons (½ stick) unsalted margarine, divided
3 cups chopped onions
½ cup low-salt chicken broth or vegetable broth
½ cup dried currants
1 tablespoon finely grated orange peel
1 tablespoon chopped fresh thyme
½ teaspoon ground cinnamon
Preheat oven to 425°F. Cut off top of baby squash (for acorn squash, cut each in half crosswise). Reserve tops. Scoop out seeds. Brush inside of squash with oil. Sprinkle with salt and pepper. Place squash, cut side down on large rimmed baking sheet. Roast squash until barely tender, about 20 minutes and 30 minutes for larger squash. Turn squash cut side up.
Toss cubed butternut squash in large bowl, with 2 tablespoons of coarse salt and pepper. Spread out on large rimmed baking sheet. Bake until tender, turning cubes once, about 45 minutes.
Melt 2 tablespoons margarine in heavy large skillet, over medium heat. Add onions. Sauté until golden, about 12 minutes. Transfer to large bowl. Add 2 tablespoons margarine and broth to skillet, stir until margarine melts. Add to onions, then mix in currants, orange peel, thyme, cinnamon, and 1 teaspoon coarse salt. Mix in squash cube. Season filling to taste with pepper. Spoon filling into squash, place tops securely on small squash.
Preheat oven to 375°F. Arrange stuffed squash on large rimmed baking sheet. Bake small squash with tops on (or acorn squash uncovered) 30 minutes. Uncover small squash, continue to bake all squash until very tender, filling is heated through, and cut surfaces brown. 10 to 20 minutes longer, depending on squash. Let stand 10 minutes. Bake leftovers along side in a dish.