Cook the wild rice in a large pot of boiling salted water until tender, about 1 hour.
Meanwhile: preheat the oven to 400°F. Toss the squash with the olive oil on a heavy large baking sheet. Sprinkle the squash with salt and roast until the squash is just beginning to brown, about 10 minutes. Stir the squash. Scatter the shallots over the squash and cook until shallots and squash are browned and tender, about 15 minutes longer. Transfer the squash mixture to a large serving bowl and keep warm.
Melt the butter in a medium skillet over medium heat. Add the brown rice and saute until heated through, about 4 minutes. Transfer the rice to the bowl with the squash mixture. Drain the wild rice and add to the bowl along with the almonds, currants and parsley and toss gently to combine. Season the stuffing to taste with salt and pepper and serve.