1. Preheat oven to 425 degree F and arrange racks in upper and lower thirds of oven. Toss together squash, brussels sprouts, turnips, and oil in a large bowl; season with salt and pepper. Divide between 2 large baking sheets, spreading into a single layer. Roast, stirring occasionally, switching baking sheets halfway through, until tender and golden brown, about 30 minutes.
2. Meanwhile, melt butter with hazelnuts in a small saucepan over moderate heat, swirling pan occasionally, until butter begins to brown, about 4 minutes. Remove pan from heat and stir in vinegar; salt and pepper to taste.
3. Transfer roasted vegetables to a serving bowl and toss with hazelnut-browned butter and tarragon. Garnish with tarragon leaves, if desired. Makes 8 servings.