I started making this recipe in 2000, when it first appeared in Bon Apetit Magazine. My family claims they won't let me come to Thanksgiving dinner unless I bring this with me! It is easy to make ahead and everyone is sure to love it.
Preheat oven to 350°F Butter 13x9x2-inch glass baking dish. Melt butter in heavy large skillet over medium-high heat. Add onions; sauté until onions are light golden, about 8 minutes. Add squash; sauté 4 minutes. Sprinkle sugar, salt and pepper over vegetables; sauté until onions and squash begin to caramelize, about 5 minutes.
Spread vegetable mixture in prepared dish. Pour chicken broth over. Cover tightly with foil and bake 45 minutes. (Squash mixture can be made 1 day ahead. Cool, then cover and refrigerate. Reheat in 350°F oven until heated through, about 10 minutes.).
Increase oven temperature to 400°F Mix breadcrumbs, cheese, rosemary and thyme in medium bowl. Sprinkle over gratin. Bake uncovered until top is golden brown and crisp, about 30 minutes.